{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def binomial_tree_price(S, K, r, T, sigma, n, option=\"call\",option_type=\"european\"):\n",
    "    #默认情况下期权是欧式看涨期权\n",
    "    \"\"\"用二叉树方法计算美式看涨或看跌期权的价格\"\"\"\n",
    "    deltaT = T / n  # 每个时间步长的长度\n",
    "    u = np.exp(sigma * np.sqrt(deltaT))  # 上涨因子\n",
    "    d = 1 / u  # 下跌因子\n",
    "    p = (np.exp(r * deltaT) - d) / (u - d)  # 上涨概率\n",
    "    disc = np.exp(-r * deltaT)  # 贴现因子\n",
    "    # 构建二叉树\n",
    "    stock_tree = np.zeros((n + 1, n + 1)) # stock_tree：创建一个 (n + 1) x (n + 1) 的矩阵来存储每个时间点的标的资产价格\n",
    "    for i in range(n + 1): # 遍历时间步长，从 i = 0 到 i = n（包括 n）\n",
    "        for j in range(i + 1): # 循环在每个时间步 i 中，遍历从 j = 0 到 j = i（包括 i）\n",
    "            stock_tree[j, i] = S * (u ** (i - j)) * (d**j) # 在时间步长 i 的第 j 个节点：有 i - j 次价格上涨（对应因子 u），有 j 次价格下跌（对应因子 d）\n",
    "    option_tree = np.zeros((n + 1, n + 1)) # option_tree：创建一个 (n + 1) x (n + 1) 的矩阵来存储每个时间点的期权价值。\n",
    "    # 计算到期时（二叉树最后一列）的期权价值\n",
    "    if option == \"call\":\n",
    "        option_tree[:, n] = np.maximum(stock_tree[:, n] - K, 0)  # 欧式看涨期权\n",
    "    else:\n",
    "        option_tree[:, n] = np.maximum(K - stock_tree[:, n], 0)  # 欧式看跌期权\n",
    "    # 从后往前递归计算每个节点的期权价值\n",
    "    for i in range(n - 1, -1, -1): # 从倒数第二列（n-1）开始，逐列向前计算期权价值，直到第 0 列\n",
    "        for j in range(i + 1): # 对于每个时间步 i，计算该时间步中每个节点 j 的期权价值\n",
    "            option_tree[j, i] = disc * (p * option_tree[j, i + 1] + (1 - p) * option_tree[j + 1, i + 1])\n",
    "    # 美式期权早期行权检查\n",
    "            if option_type == \"american\":\n",
    "                if option == \"call\":  \n",
    "                    option_tree[j, i] = np.maximum(option_tree[j, i], stock_tree[j, i] - K)\n",
    "                else:\n",
    "                    option_tree[j, i] = np.maximum(option_tree[j, i], K - stock_tree[j, i])\n",
    "    # 绘制二叉树图像\n",
    "    fig, ax = plt.subplots(figsize=(12, 8))\n",
    "    \n",
    "  # 绘制标的资产价格节点及期权价格\n",
    "    for i in range(n + 1):\n",
    "        for j in range(i + 1):\n",
    "            ax.text(i, j - i / 2, f'S={stock_tree[j, i]:.2f}\\nV={option_tree[j, i]:.2f}', ha='center', va='center', \n",
    "                    bbox=dict(facecolor='lightblue', edgecolor='black', boxstyle='round,pad=0.5'))\n",
    "    \n",
    "    # 添加连线\n",
    "    for i in range(n):\n",
    "        for j in range(i + 1):\n",
    "            ax.plot([i, i + 1], [j - i / 2, j - i / 2 - 1 / 2], 'k-')\n",
    "            ax.plot([i, i + 1], [j - i / 2, j - i / 2 + 1 / 2], 'k-')\n",
    "\n",
    "    # 设置标题和轴标签\n",
    "    ax.set_title(\"Binomial Tree for Stock Prices\")\n",
    "    ax.set_xlabel(\"Time Step\")\n",
    "    ax.set_ylabel(\"Price Level\")\n",
    "    \n",
    "    # 调整坐标轴\n",
    "    ax.set_xlim(-0.5, n + 0.5)\n",
    "    ax.set_ylim(-n / 2 - 0.5, n / 2 + 0.5)\n",
    "    \n",
    "    # 隐藏坐标轴刻度\n",
    "    ax.set_xticks(np.arange(n + 1))\n",
    "    ax.set_yticks([])\n",
    "    \n",
    "    plt.gca().invert_yaxis()\n",
    "    plt.show()\n",
    "    # 返回期权价格\n",
    "    return option_tree[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期权价格: 7.428401902704835\n"
     ]
    }
   ],
   "source": [
    "#测试\n",
    "S = 50\n",
    "K = 52  \n",
    "r = 0.05 \n",
    "T = 2.0  \n",
    "sigma = 0.3\n",
    "n = 2  \n",
    "\n",
    "price = binomial_tree_price(S, K, r, T, sigma, n, option=\"put\", option_type=\"american\")\n",
    "print(\"期权价格:\", price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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g4+OD7du348MPP0RAQADGjRsHABgxYgQeeeQRvP/++8jIyEBQUBDMzc2xf/9+WFlZYdasWdX6U6vVsLKyglqtRklJCVatWiWW+d8vCxcuxNq1azFy5EjMmzcPPj4+yM3Nxbp16zBnzhx07dq1xt8f8+fPx6VLlzB27Fh4eHggNzcXX331FUxNTevsvt1ERFQ7DM5ERM3AE088If5ub2+P9u3b4/PPP8dzzz1XZ4+xdOlSdOjQAcuXL8d3330He3t7+Pn5YdGiRdU+I12XTE1NERMTgxdeeAEzZsyAiYkJxo0bh02bNqFt27b19ri3Ym1tjcTERHz00Uf44YcfcPbsWVhaWqJt27YYN26czozi999/j8GDB+P777/HkiVLoNVq4ebmhmHDht310vmHHnoI1tbWWLRoEaZOnQpjY2MMHjwYCQkJGDp06F0/r1mzZuHPP//Ejz/+iMuXL6OoqAjOzs4YMmQIfv31VwwePFjs+8ILLyAlJQXz5s1DXl4eFEWBoiiwsLBAQkIC3nzzTXz66afIysqCu7s7XnnllWr3Xf7ll1/Qt29fLF++HL/88gssLS3RrVs3zJs377Y9BgQEYM2aNQgODkZoaCgiIiJuecus+uLu7o5du3bhnXfewUcffYScnBw4Oztj+PDh4rP7Nf3+GDRoEPbs2YO5c+ciKysLDg4O6N+/P+Lj49G9e/f79pyIiOh/VMrN67mIiIiIiIiISAc/40xERERERESkB4MzERERERERkR4MzkRERERERER6MDgTERERERER6cHgTERERERERKQHgzMRERERERGRHg3iPs5arRZpaWmwtbWFSqUydDtERERERETUxCmKgoKCAri5ucHISP+ccoMIzmlpaWjTpo2h2yAiIiIiIqJm5uLFi/Dw8NC7T4MIzra2tgCuN2xnZ2fgboiIiIiIiKipy8/PR5s2bUQe1adBBOcby7Pt7OwYnImIiIiIiOi+qcnHhXlxMCIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDwZnIiIiIiIiIj0YnImIiIiIiIj0YHAmIiIiIiIi0oPBmYiIiIiIiEgPBmciIiIiIiIiPRiciYiIiIiIiPRgcCYiIiIiIiLSg8GZiIiIiIiISA8GZyIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDwZnIiIiIiIiIj0YnImIiIiIiIj0YHAmIiIiIiIi0oPBmYiIiIiIiEgPBmciIiIiIiIiPRiciYiIiIiIiPRgcCYiIiIiIiLSg8GZiIiIiIiISA8GZyIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDwZnIiIiIiIiIj0YnImIiIiIiIj0YHAmIiIiIiIi0oPBmYiIiIiIiEgPBmciIiIiIiIiPRiciYiIiIiIiPRgcCYiIiIiIiLSg8GZiIiIiIiISA8GZyIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDwZnIiIiIiIiIj0YnImIiIiIiIj0YHAmIiIiIiIi0oPBmYiIiIiIiEgPBmciIiIiIiIiPRiciYiIiIiIiPRgcCYiIiIiIiLSg8GZiIiIiIiISA8GZyIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDwZnIiIiIiIiIj0YnImIiIiIiIj0YHAmIiIiIiIi0oPBmYiIiIiIiEgPBmciIiIiIiIiPRiciYiIiIiIiPRgcCYiIiIiIiLSg8GZiIiIiIiISA8GZyIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDwZnIiIiIiIiIj0YnImIiIiIiIj0YHAmIiIiIiIi0oPBmYiIiIiIiEgPBmciIiIiIiIiPRiciYiIiIiIiPRgcCYiIiIiIiLSg8GZiIiIiIiISA8GZyIiIiIiIiI9GJyJiIiIiIiI9GBwJiIiIiIiItKDwZmIiIiIiIhIDxNDN0BERERERA1HVVUV9u7diytXrqCoqMjQ7dxXKpUKtra28PT0RI8ePaBSqQzdEjUQDM5ERERERITDhw9j2bJl0ISHIzMjw9DtGJxXhw6Y+sADeO655+Dh4WHodsjAGJyJiIiIiJq5HTt2YMLEibCwtsFgv1AMmRiAVm3bw8LKGs1p0lWrVVBSWIDzJ49jx/oYfLtkKVb+/ju2btmCdu3aGbo9MiCVoiiKoZvIz8+Hvb098vLyYGdnZ+h2iIiIiIiajQMHDmDEyJFo26Ub5n3/GyytrQ3dUoORfeUyFjwmwVSlYFdyMlxdXQ3dEtWh2uRQXhyMiIiIiKgZ++qrr2Dj0JKh+RacWrtjwb9lpKen4z//+Y+h2yEDYnAmIiIiImqmysvLERkVheFBkxmab8OptTt6jxiNv/6SDd0KGRCDMxERERFRM7V9+3bk5eZi8IQAQ7fSoA2ZGITdu3chPT3d0K2QgTA4ExERERE1U5cvXwYAuLXvYOBOGja3dtdfnytXrhi4EzIUBmciIiIiomaqsLAQxsbGMLewNHQrDZqVjQ0AoKCgwMCdkKEwOBMRERERNWfN6X5Td4uvUbPH+zgTEREREZFeeTnZWPXVJ9ifGI/c7GzY2NvDs0s3TH3+ZXTp07/W4x3akYg/vvoE508eh4W1NXxD1XjoxddhbHI9npSXleL7d17HmZRDuHTmFPr5jsPr362447iaZV9h35ZNOHs8BSamZvjP7uPV9ln+wds4vncXLpw6AY8OHfFZ1KZa90/ND4MzERERERHp9ensp1BZWYnnF30F1zaeyMvJwuEd21GYl1vrsc6dOIoPnn4EYc/MxqyPv8bVjHR8v2AutFVVeGzuOwAAbZUWZhYWCHjk/7BzQ1yNx64sL8cQv2B07t0fm8NX3XonRcGYsGk4dWg/zp84Wuv+qXlicCYiIiIiotsqys/Dsb27sPDXcHQfOAQA4OLugU49+9zVeElx0fDs4o0HZs4BALT2bI/pc97Aly/PxAMzX4aljQ0srKwwY8FHAIDj+3ajqCCvRmNPm/0qACA+4s/b7vN/b70PAMi/msPgTDXG4ExERERERLdlYWUNCytr7Nq8Dp1794WpmXm1fd7/13Qc25usd5yV+04DACrKy2FmrjuGmbklystKkZpyCD0GDa275onqCIMzERERERHdlrGJCZ5f9CWWzX8VG/74D9p364HuA4ZgWGAo2nXpBgB49v3FKC8trdF4vYePQtyvPyIxNhJD/UOQm52J8GVfAgCuZWXU19MguicMzkREREREpNeQiYHo5zsWx/Yk48SBvTiQmICo5Uvw7HuLMWbKVDi6tq7xWL2H++KRV9/GDwtex9dzZ8PUzAzqZ1/Esb27YGRsXI/PgujuMTgTEREREdEdmZlboNewUeg1bBQemDkHS956GX9+ez0412apNgCEPDEDwY8/jWuZGbC2t0fW5UtY+fkiuHq0re+nQXRXGJyJiIiIiKjWPDp0xq5N6wDUbqn2DSqVCi1dWwEAEuMi4dTaDe27+dR5n0R1gcGZiIiIiIhuq+DaVSx+cQbGhE2DZxdvWFrbIPXIQUQvX4IBYycCQK2WagNA1PIl6DN8NFRGRkjeuAZRP36HOV8sg/FNS7Uvnj6JyopyFOZdQ0lREc4eOwIAaO/dAwBw6tB+fD13Nhb88pd4/Ky0SyjMy0X2lcvQVlWJY1q1bQ9La2sAwJXzZ1FaXITc7CyUl5aKfTw6dIapmdk9vFLUlDE4ExERERHRbVlYW6NTzz6I/eUHpF88j6rKCji2csM4aTqmzJh1V2Pu35aA8GVfo7K8HJ5du2HudyvQd+QYnX0+ePphZKVdEl+/MnkCACD8eBoAoKykBGlnU1FVUSn2+ePrxdgS9Ve1Y979t0ZcrXvpW68gZfeOavss3ZQMF482d/V8qOlTKYqiGLqJ/Px82NvbIy8vD3Z2doZuh4iIiIioWVi6dClmzZ6Nv45cMHQrDVrauTOY5TccW7duxciRIw3dDtWR2uRQo/vUExEREREREVGjxOBMREREREREpAeDMxEREREREZEeDM5EREREREREejA4ExEREREREenB4ExERERERDXy4TOPYsETD9yydmL/HoR1dcOZlEO1Hjdl1w68OmUipvVsj2fHDcb6P3694zFZaZfw4TOP4qE+HfD44O5Y/v5bqCgv19nn/IljePvhKXiwlxf+NbIv/vruczSAmwpRI8TgTERERERENTJW/SCO7ExC5uVL1WrxEX+gvXd3eHXvWasxMy5dwAczHoZ3/0FYHLkBYTNm4ecP3saO9XG3PaaqqgofzngUZSUleH9lFF76fCl2bliDf3/8rtinuLAAC/9vGlq4uOJjeQ3+7633sfrnZYhZ8X2t+iMCGJyJiIiIiKiG+vuOh72jE7ZE/qmzvaykGElrVmNM2IO1HnPDH7/CqbU7npy3EB4dOmGcNB1jpkzD6p+X3faYg0lbcSn1JF745Bt4dfNBr6Ej8djc+dgk/47iwgIAwLaYCJSXlWHWR1+ibeeuGDwhAFNmzELMLz9w1plqzcTQDRARERERUeNgbGKCUaFqJET+BWnmHKhUKgDA3+tiUVlRgZHBUwAA0/t21DuOd79BeOvHlQCAEwf2otewUTr13sN9sTl8FSorKmBialrt+BMH9qBNp65o6dpK55iK8jKkHjkEn8HDcPLAXnQfMBimZuY6+6z8fBEyL1+Eq0fbu3sRqFlicCYiIiIiohobEzYN0cuX4kjy3/AZPAwAEB/+BwaN94eNvQMAYHHkRr1jmFlYiL/nZmXBYbizTt3e0QlVlZUouHYVLVxcqx2fm5UFB0cnnW029g4wMTVDbnbmf/fJhLN7G519HBydRY3BmWqDwZmIiIiIiGrMw6sTuvTpj/iIP+AzeBjSL5zDsb3JeHv5KrFPa8/2tRrzxsz1/yg3CvoOusVGRWesf46r/Hfc6o9HpB+DMxERERER1cpY9YP46b038a/5HyI+4k84u3mg55ARol6bpdoOzs649t9Z4hvycnJgbGICW4cWtzzewdkZpw7t19lWmJeLyooK2P93VtnB2UXMPv9v3GwAgL2T7gw30Z0wOBMRERERUa0M9QvBzx/MR2JsJLZE/YVx0nSdWdzaLNXu0rsf9iTo7n8gaSs6dO91y883Xz+mPyKWfY1rmRliKffBpK0wNTNHhx7Xr+rduXc//P7FR6goL4epmZnYp6VLK7j8Ywk30Z3wqtpERERERM1URkYGcBdXmLa0tsawgBD8/sVHuJaZgdGTde/t3Nqzvd4/jq6txb4Tpj2KrLRLWLFoAS6lnsLm8FWID1+FkCefEfskb1yLWf7/m9HuNWwUPDp0xldzZ+HM0cM4tCMR//5kIcZJD8HKxhYAMCJoMkzNzPDtGy/iwsnjSN64FhHff4Pgx5/mUm2qNc44ExERERE1I8eOHYMsy5BlGUeOHIGRkfFdjTM27EFs1qxCr2Gj4Ozmcdf9uHq0xZvf/4YVH72Ddb//gpYurnjyzfcwZGKg2KeoIB9pZ1PF18bGxpj3/a/48d15ePOhUJiZW2JE0CQ8Nne+2Mfa1g7zl/+BH9+bh9fU/rC2t0fw408j+IkZd90rNV8qpQHcxCw/Px/29vbIy8uDnZ2dodshIiIiImpSUlJSoNFoIMsyUlJSxHYjIyNApYKcctGA3TV8aefOYJbfcGzduhUjR440dDtUR2qTQznjTERERETUxCiKgpSUFDGzfOzYMVEzNTXF+PHjIUkScnJyMPf11w3YKVHjwOBMRERERNQEKIqCw4cPQ5ZlaDQaHD9+XNTMzMwwYcIESJKEkJAQODg4AACWLVsGRauFoij83K8eWm0VgP/O0FOzxOBMRERERNRIKYqCgwcPimXYJ0+eFDUzMzP4+flBrVYjJCQE9vb21Y63t7eHVqtFaVERLG1s7mfrjUpxfj4A3PI1pOaBwZmIiIiIqBFRFAUHDhwQy7BPnz4taubm5vDz84MkSQgODr7j5zY7deoEADh95CB8Bg+r174bs9NHDsLExARt2vA2Vs0VgzMRERERUQOnKAr27dsnlmGnpv7vCtMWFhbw9/eHJEkIDAys1cV2+/Xrh7aentixPpbBWY8d62Iwbtx4scSdmh8GZyIiIiKiBkhRFOzZswcajQYajQZnzpwRNUtLSwQEBECtViMwMBC2trZ39RgqlQqSWo0fl/+MkCdmoFXbdnXUfdORsnsnju3dhVeWLzd0K2RAvB0VEREREVEDoSgKdu/eLWaWz507J2qWlpYIDAyEJEkICAiATR19JvnKlSsYNcoX1woK8fbyVfDo0KlOxm0KDu1IxCczn8TgwYMQFxsLS0tLQ7dEdYi3oyIiIiIiaiQURUFycrIIyxcuXBA1KysrBAUFQZIk+Pv7w9raus4fv3Xr1ti6dQtGjfLFC4Gj0KV3PwwaH4BWbdvBwtq6WV1tW9FqUVxQgAunjmPn+lhcOH0So8eMQWxMDENzM8fgTERERER0n2m1WuzcuVMsw7548aKoWVtbIzg4GGq1Gv7+/rCysqr3flq3bo29e/dg9erV+EuW8cdXH6O8vLzeH7ehsrWzw6TQUEifL8bEiRNhZmZm6JbIwLhUm4iIiIjoPtBqtdixYwdkWUZ4eDguXbokajY2NggODoYkSfDz8zP47GZFRQVyc3NRWFho0D7uN5VKBTs7O9jb28PY2NjQ7VA941JtIiIiIqIGQKvVIikpSYTltLQ0UbO1tUVISAgkScKECRMMHpZvZmpqCmdnZzg7Oxu6FaIGgcGZiIiIiKgOVVVV6YTlK1euiJqdnR1CQ0OhVqsxYcIEWFhYGLBTIqopBmciIiIiontUVVWFxMREyLKMiIgIpKeni5q9vT1CQ0MhSRLGjx8Pc3NzA3ZKRHeDwZmIiIiI6C5UVlZi27ZtIixnZmaKmoODAyZNmgRJkjB27FiGZaJGjsGZiIiIiKiGKisrsXXrVhGWs7KyRK1FixY6YZlXYiZqOhiciYiIiIj0qKysREJCAmRZRmRkJLKzs0WtZcuWmDx5MiRJwpgxY2BqamrATomovjA4ExERERH9Q0VFBeLj4yHLMqKiopCTkyNqjo6OmDJlCiRJgq+vL8MyUTPA4ExEREREBKC8vFwnLF+9elXUnJycdMKyiQlPo4maE/6PJyIiIqJmq7y8HJs2bYIsy4iOjsa1a9dEzcXFRYTlkSNHMiwTNWP8309EREREzUpZWRk2btwownJeXp6oubq6IiwsDJIkYcSIETA2NjZgp0TUUDA4ExEREVGTV1paKsLy6tWrdcJyq1atRFgePnw4wzIRVcPgTERERERNUmlpKdavXy/CckFBgai5ubmJsDx06FCGZSLSi8GZiIiIiJqMkpISrFu3DhqNBjExMTph2d3dHWq1Gmq1GkOHDoWRkZEBOyWixoTBmYiIiIgateLiYqxbtw6yLCM2NhaFhYWi5uHhAbVaDUmSMHjwYIZlIrorDM5ERERE1OgUFxdjzZo1kGUZcXFxKCoqErW2bduKsDxw4ECGZSK6ZwzORERERNQoFBUVIS4uDhqNBnFxcSguLhY1T09PSJIEtVqNgQMHQqVSGbBTImpqGJyJiIiIqMEqLCxEXFwcZFnGmjVrUFJSImrt2rWDJEmQJAn9+/dnWCaiesPgTEREREQNSkFBAWJjYyHLMtauXYvS0lJR8/LyEmG5b9++DMtEdF8wOBMRERGRweXn5yMmJgYajQZr165FWVmZqHXs2FEsw+7Tpw/DMhHddwzORERERGQQeXl5iImJgSzLWL9+vU5Y7tSpk5hZ7tWrF8MyERkUgzMRERER3Te5ublYvXo1ZFnGhg0bUF5eLmpdunQRYdnHx4dhmYgaDAZnIiIiIqpX165dQ3R0NDQaDTZs2ICKigpR8/b2Fsuwe/TowbBMRA0SgzMRERER1bmrV68iOjoasixj06ZNOmG5W7duYma5e/fuBuySiKhmGJyJiIiIqE7k5OQgKioKsixj8+bNqKysFLUePXqImeVu3boZsEsiotpjcCYiIiKiu5adnY3IyEhoNBps3rwZVVVVotazZ08Rlrt27WrALomI7g2DMxERERHVSlZWFiIjIyHLMhISEnTCcq9evcQy7M6dOxuwSyKiusPgTERERER3lJmZiYiICMiyjC1btkCr1Ypanz59xMxyp06dDNglEVH9YHAmIiIioltKT09HREQENBoNtm7dqhOW+/XrB0mSEBYWho4dOxqwSyKi+sfgTERERETClStXxMzytm3boCiKqPXv31/MLHt5eRmwSyKi+4vBmYiIiKiZS0tLQ3h4OGRZxvbt23XC8sCBA0VYbteuneGaJCIyIAZnIiIiombo8uXL0Gg00Gg0SEpK0gnLgwcPFsuwPT09DdglEVHDwOBMRERE1ExcvHhRzCz//fffOrUhQ4aIsNy2bVsDdUhE1DAxOBMRERE1YRcuXIBGo4Esy9i5c6dObdiwYSIse3h4GKhDIqKGj8GZiIiIqIk5d+6cmFlOTk4W21UqFYYPHw61Wo2wsDC4u7sbsEsiosaDwZmIiIioCTh79qyYWd69e7fYrlKpMGLECEiShClTpsDNzc2AXRIRNU4MzkRERESN1JkzZyDLMmRZxt69e8V2IyMjjBw5UoTlVq1aGbBLIqLGj8GZiIiIqBE5ffq0mFnet2+f2G5kZARfX1+o1WpMmTIFrq6uBuySiKhpYXAmIiIiauBOnTolZpYPHDggthsZGWH06NGQJAmTJ0+Gi4uL4ZokImrCGJyJiIiIGqATJ06IsHzo0CGx3djYGGPGjIEkSZg0aRKcnZ0N2CURUfPA4ExERETUQBw7dkwswz58+LDYbmJigrFjx0KtVmPSpElwcnIyYJdERM0PgzMRERGRAR09elTMLKekpIjtJiYmGDduHCRJQmhoKBwdHQ3YJRFR88bgTERERHQfKYqClJQUEZaPHTsmaqamphg/frwIyy1atDBgp0REdAODMxEREVE9UxQFhw8fFsuwjx8/LmpmZmaYMGECJElCcHAwwzIRUQPE4ExERERUDxRFwaFDh8TM8smTJ0XNzMwMfn5+UKvVCAkJgb29vQE7JSKiO2FwJiIiIqojiqLgwIEDkGUZGo0Gp06dEjVzc3P4+fmJmWU7OzsDdkpERLXB4ExERER0DxRFwb59+8Qy7NTUVFGzsLCAv78/JElCYGAgwzIRUSPF4ExERERUS4qiYO/evWJm+cyZM6JmaWmJgIAAqNVqBAYGwtbW1oCdEhFRXWBwJiIiIqoBRVGwe/duEZbPnTsnapaWlggMDIQkSQgICICNjY3hGiUiojrH4ExERER0G4qiIDk5GRqNBhqNBufPnxc1KysrBAUFQZIk+Pv7w9ra2oCdEhFRfWJwJiIiIrqJVqtFcnKymFm+ePGiqFlbWyM4OBhqtRr+/v6wsrIyYKdERHS/MDgTERFRs6fVarFjxw7Isozw8HBcunRJ1GxsbBAcHAxJkuDn5wdLS0sDdkpERIbA4ExERETNklarRVJSEjQaDcLDw3H58mVRs7W1RUhICCRJwoQJExiWiYiaOQZnIiIiajaqqqqQlJQkZpavXLkianZ2dggNDYVarcaECRNgYWFhwE6JiKghYXAmIiKiJq2qqgqJiYmQZRkRERFIT08XNXt7e4SGhkKSJIwfPx7m5uYG7JSIiBoqBmciIiJqciorK3XCckZGhqg5ODhg0qRJkCQJY8eOZVgmIqI7YnAmIiKiJqGyshJbt24VYTkrK0vUWrRooROWzczMDNgpERE1NgzOREREd+nGEuC4uDhcuXIFRUVFhm7pvlKpVLC1tYWnpycmT56M3r17Q6VS3dceKisrkZCQAFmWERkZiezsbFFr2bIlJk+eDEmSMGbMGJiamt7X3oiIqOlQKYqiGLqJ/Px82NvbIy8vD3Z2doZuh4iI6I4WL16MTxcvRmZGBpxatYZrG0+YW1oB9zk4GpKi1aK0qBCXz5xGfu41eHXogI8WLYIkSfX6uBUVFTphOScnR9QcHR0xZcoUSJIEX19fhmUiIrqt2uRQzjgTERHV0oIFC/Duu+9i/AMPY8yUqejUq+99n2ltSCorKnAkOQlrV67AtGnTUFlZiQcffLBOH6OiogKbN2+GLMuIiorC1atXRc3JyUknLJuY8PSGiIjqFmeciYiIamHlypV4+OGHMX3OG5jy9CxDt9OgVFVVYcmbL2Pbag127tyJAQMG3NN45eXl2LRpE2RZRnR0NK5duyZqLi4uIiyPHDmSYZmIiGqNM85ERET1ZMWKX+AzeDhD8y0YGxvjuQ8+w+Ed27By5cq7Cs5lZWU6YTk3N1fUXF1dERYWBkmSMGLECBgbG9dh90RERLfH4ExERFRDWVlZSEiIx7/mLzJ0Kw2WsbExBo0PwF+yjM8//xxGRkZ3PKasrAwbNmyALMtYvXo18vLyRK1Vq1YiLA8fPpxhmYiIDILBmYiIqIaSkpKg1WrRz3esoVtp0Pr5jsOa335GamoqOnXqdMt9SktLsX79emg0GqxevRr5+fmi5ubmJsLy0KFDGZaJiMjgGJyJiIhq6MYFqRycXAzcScPm4Hz99bn5Al4AUFJSgvXr10OWZcTExKCgoEDU3N3doVaroVarMXTo0BrNVBMREd0vDM5EREQ1VFZWBmMTExjzQlR6mZlbALj+epWUlGDt2rWQZRmxsbEoLCwU+3l4eECtVkOSJAwePJhhmYiIGiz+5CciIqJ6sWDBAuzatQtFRUViW9u2bUVYHjhwIMMyERE1CgzOREREdSwvJxurvvoE+xPjkZudDRt7e3h26Yapz7+MLn3639WY8RF/IuaXH3Dl3BlY29lh8IRA/Gv+hwCAP79ZjL+++7zaMeaWlvh9f+odx64oL8PrDwTi3PGjWBy5Ae29e4jaoR2J+OOrT3D+5HFYWFvDN1SNh158vUaz7gkJCQAAT09PSJIEtVqNgQMHNut7XhMRUePE4ExERFTHPp39FCorK/H8oq/g2sYTeTlZOLxjOwrzcu9qvNUrvkfMiu/x6KtvoVOvvigvK0PGxfOiHvLks5gw7VGdYxY88QA69uhdo/F//fR9tHBphXPHj+psP3fiKD54+hGEPTMbsz7+Glcz0vH9grnQVlXhsbnv3HHcadOmYc6cOejfvz/DMhERNWoMzkRERHWoKD8Px/buwsJfw9F94BAAgIu7Bzr17HNX4xXm5WLVVx/jjaX/Rs8hI8T2tp26iL9bWlvD0tpafH3ueAounT6JGQs+vuP4+7bF42DSVrz69U/Yvy1ep5YUFw3PLt54YOYcAEBrz/aYPucNfPnyTDww82VY2tjoHfvZZ5+9q3s5ExERNTQMzkRERHXIwsoaFlbW2LV5HTr37gtTM/Nq+7z/r+k4tjdZ7zgr950GABz8exsUrYKrGemYHTASJUVF6NKnPx6fOx9Ord1veewm+Xe4tfNCt/6D9D5GbnYWlr79KuZ++zPMLSyr1SvKy2Fmrtu/mbklystKkZpyCD0GDdU7PhERUVPB4ExERFSHjE1M8PyiL7Fs/qvY8Md/0L5bD3QfMATDAkPRrks3AMCz7y9GeWlpjcbLuHgeiqJF+Pdf48l578Ha1ha/f/Ux3n1yGj6P3gxTMzOd/SvKy5AYG4nJ/5qpd1xFUfDtGy9i4rRH0NGnFzIvXay2T+/hoxD3649IjI3EUP8Q5GZnInzZlwCAa1kZNeqfiIioKWBwJiIiqmNDJgain+9YHNuTjBMH9uJAYgKili/Bs+8txpgpU+Ho2rrGYylaBZUVFfi/N99D7+G+AICXPluKp4b3wpHkv9FnhK/O/js3rEFJUSFGhUp6x13zn+UoLizA5Kdn3Xaf3sN98cirb+OHBa/j67mzYWpmBvWzL+LY3l0wMjau8XMgIiJq7BiciYiI6oGZuQV6DRuFXsNG4YGZc7DkrZfx57fXg3Ntlmq3cHYBALTp2FnU7Fs6wrZFS2RfuVztuM2aVejnO04cdzuHk5Nw6uA+TOvZTmf7a2p/jAyaglkffwUACHliBoIffxrXMjNgbW+PrMuXsPLzRXD1aHvH14CIiKipYHAmIiK6Dzw6dMauTesA1G6pdte+1y+udflsKhxbuQEACnKvoeDaVTi76X7GOePSBRxJTsLrS36547j/9+Z7eOiFueLrq5npeO+phzDn82Xo3Ev3QmYqlQotXVsBABLjIuHU2g3tu/nUqH8iIqKmgMGZiIioDhVcu4rFL87AmLBp8OziDUtrG6QeOYjo5UswYOxEAKjVUm239h0wYOxE/PzhfDzz7iewsrHFb59/CDevjugxaJjOvvHhf6CFsyv6jBxTbZxTh/bj67mzseCXv+Do2hrObh46dQur61flbtXWUwR0AIhavgR9ho+GysgIyRvXIOrH7zDni2Uw5lJtIiJqRhiciYiI6pCFtTU69eyD2F9+QPrF86iqrIBjKzeMk6Zjyozbf55Yn9kff40Vi97Bh888CpXKCN0HDsbbP66Eiamp2Eer1SIh8k/4Tn7glqG2rKQEaWdTUVVRWavH3r8tAeHLvkZleTk8u3bD3O9WoO8tgjkREVFTplIURTF0E/n5+bC3t0deXh7s7OwM3Q4REdEtLV26FLNmz8ZfRy4YupUGLe3cGczyG46tW7di5MiRhm6HiIjolmqTQ43uU09EREREREREjRKDMxEREREREZEeDM5EREREREREejA4ExEREREREenB4ExERERERESkB4MzERFRPfnwmUex4IkHblk7sX8Pwrq64UzKoVqPm7JrB16dMhHTerbHs+MGY/0fv97xmEM7EjFvWjCm9+2E/xvRG/9Z/D6qKv93a6rLZ05j/qNqPDmspxj39y8/RmVFRa37IyIiamp4H2ciIqJ6Mlb9ID6d9RQyL1+Ci7uHTi0+4g+09+4Or+49azVmxqUL+GDGwxgnTccLn36L4/t24ceF82DXwhFDJgbe8phzJ47ig6cfQdgzszHr469xNSMd3y+YC21VFR6b+w4AwNjUFL6hanh194GVrT3On0jB0rdfhaLVYvqcN+7uBSAiImoiGJyJiIjqSX/f8bB3dMKWyD/xwPMvi+1lJcVIWrMaD730eq3H3PDHr3Bq7Y4n5y0EAHh06ITUI4ew+udltw3OSXHR8OzijQdmzgEAtPZsj+lz3sCXL8/EAzNfhqWNDVq18USrNp7iGBd3DxxJ3oFje5Nr3SMREVFTw+BMRERUT4xNTDAqVI2EyL8gzZwDlUoFAPh7XSwqKyowMngKAGB63456x/HuNwhv/bgSAHDiwF70GjZKp957uC82h69CZUUFTExNqx1fUV4OM3NznW1m5pYoLytFasoh9Bg0tNoxV86fxYHtCRg0PqDmT5iIiKiJYnAmIiKqR2PCpiF6+VIcSf4bPoOHAQDiw//AoPH+sLF3AAAsjtyodwwzCwvx99ysLDgMd9ap2zs6oaqyEgXXrqKFi2u143sPH4W4X39EYmwkhvqHIDc7E+HLvgQAXMvK0Nl33rRgnDl6BBXlZRj/wMOYNvvV2j5lIiKiJofBmYiIqB55eHVClz79ER/xB3wGD0P6hXM4tjcZby9fJfZp7dm+VmPemLn+H+VG4Zb79x7ui0defRs/LHgdX8+dDVMzM6iffRHH9u6CkbGxzr5zvliGkqIinDuegl8/fR+rf16KSU/NrFV/RERETQ2DMxERUT0bq34QP733Jv41/0PER/wJZzcP9BwyQtRrs1TbwdkZ17Izdep5OTkwNjGBrUOL244R8sQMBD/+NK5lZsDa3h5Zly9h5eeL4OrRVmc/p9buAIA2HTtDq9Vi2fxXEfzEMzD+R8AmIiJqThiciYiI6tlQvxD8/MF8JMZGYkvUXxgnTdeZNa7NUu0uvfthT4Lu/geStqJD9163/HzzzVQqFVq6tgIAJMZFwqm1G9p387nt/oqiXL9llaLoHZeIiKipY3AmIiKqgePHj2PNmjVQ7iJEWlpbY1hACH7/4iMUF+Rj9GTdezvXZqn2hGmPYu3KFVixaAHGPzAdJw7sQXz4Kry4eInYJ3njWvz2+Yf4Zm2i2Ba1fAn6DB8NlZERkjeuQdSP32HOF8vETPK2mAgYm5jAs7M3TMzMcCblEFZ+vgjD/ENgbHJ3pwsajQYdOnSAu7v7XR1PRETUUDA4ExER3cbRo0chyzJkWUZKSgoAwMjo7pYsjw17EJs1q9Br2Cg4u3nc+YDbcPVoize//w0rPnoH637/BS1dXPHkm+/p3IqqqCAfaWdTdY7bvy0B4cu+RmV5OTy7dsPc71ag78gxom5sbIyoH79D2rkzABQ4uXnA/6HHEfT4v+6612+++QbffPMNhg4dCkmSEBYWhjZt2tz1eERERIaiUu7mV+d1LD8/H/b29sjLy4OdnZ2h2yEiomZKURSkpKRAo9FAlmUcPXpU1ExMTNC5c2ecOHESf6VcMGCXDV/auTOY5TccPXr0wJEjR3RqgwcPhiRJUKvVaNu27W1GICIiqn+1yaFG96knIiKiBklRFBw+fBjz589Ht27d4OPjg3fffRdHjx6FqakpAgMDsWLFCmRmZuL5558Hbn3harqF7777DpcuXcJXX32F4cOHQ6VSYefOnXj55Zfh6emJwYMH47PPPsO5c+cM3SoREZFeXKpNRETNjqIoOHToEGRZhkajwYkTJ0TNzMwMEyZMgCRJCAkJgYODg6iZmpqiqrISVVVVvMq0HpXl5QCuv17u7u6YPXs2Zs+ejbS0NERERECWZSQmJiI5ORnJycl45ZVXMGDAADET3b597W7PRUREVN8YnImIqFlQFAUHDhwQy7BPnTolamZmZvDz84MkSQgODoa9vf0tx2jR4vrtngquXYWDk/N96bsxyruaA+B/r9cNbm5ueP755/H888/jypUriIiIgEajwbZt27B7927s3r0br732Gvr16wdJkiBJEry8vAzxFIiIiHTwM85ERNRkKYqC/fv3i5nl06dPi5q5uTn8/f2hVqsRHBxco58/ly5dQps2bTDr46/hG6quz9Ybtf8sfh+JUX8h/coVmNTgitwZGRliJnrr1q3QarWi1rdvXzET3bGj/vtdExER1UZtciiDMxERNSmKomDv3r0iLJ85c0bULCws4O/vD0mSEBQUBFtb21qPP3ToMFRaWOP1pf+uy7abDEVR8PyEIQj2m4gffvih1sdnZmYiMjISsiwjISFBJ0T37t1bzER36tSpLtsmIqJmiMGZiIiaFUVRsHv3bmg0Gmg0Gpw9e1bULC0tERAQAEmSEBgYCBsbm3t6rCVLllxfbrzoS/hOku619SZFURT8/sVHiPjhGyQkJMDX1/eexsvKykJkZCQ0Gg3i4+NRVVUlaj179hQhukuXLvfYORERNUcMzkRE1OQpioJdu3aJmeXz58+LmpWVFQIDA6FWqxEQEHDPYflmWq0WTz/9NH7++WdMnfUKfCdJ93Rf5qbiwqkTWPOf5dj412/47LPPMGfOnDodPzs7G1FRUZBlGZs3b9YJ0T4+PmI5t7e3d50+LhERNV0MzkRE1CRptVokJyeLsHzx4kVRs7KyQlBQECRJgr+/P6ytreu1j5deegnLli1DeXk5OvfsA5c2nrC0toFK1XzuV6XValFcmI+LJ4/jYuop2NrZ4f333sPs2bPr9XFzcnIQHR0NWZaxadMmVFZWilr37t3FTHS3bt3qtQ8iImrcGJyJiKjJ0Gq12LFjh1iGfenSJVGztrZGcHAwJEmCn58frKys7mtveXl5iImJQVxcHK6kp6OgoPC+Pr6hqVSAvb09PNu2xeTJkzFhwgSYm5vf1x6uXr2K6OhoaDQabNy4ERUVFaLm7e0tQnT37t2b1S81iIjozhiciYioUdNqtfj7778hyzLCw8Nx+fJlUbOxsUFISAjUajX8/PxgaWlpwE6pIbl27RpWr14NWZaxYcMGnRDdtWtXsZzbx8eHIZqIiBiciYio8amqqkJSUpIIy1euXBE1W1tbhISEQJIkTJw4ERYWFgbslBqD3NxcxMTEQJZlrF+/HuXl5aLWuXNnMRPds2dPhmgiomaKwZmIiBqFqqoqbN++XYTl9PR0UbOzs0NoaCgkScL48eMZlumu3VhSr9FosG7dOpSVlYlap06doFarIUkSevfuzRBNRNSMMDgTEVGDVVVVhW3btkGWZURERCAjI0PU7O3tdcLy/f68LDV9+fn5iI2NhSzLWLt2rU6I7tChg1jO3bdvX4ZoIqImjsGZiIgalMrKSmzduhWyLCMyMhKZmZmi5uDggEmTJkGSJIwbNw5mZmYG7JSak4KCAsTFxUGWZaxZswalpaWi5uXlJWai+/XrxxBNRNQEMTgTEZHBVVZWYsuWLSIsZ2VliVqLFi0wefJkSJKEMWPGMCyTwRUWFiIuLg4ajQZxcXEoKSkRtXbt2okQPWDAAIZoIqImgsGZiIgMoqKiAgkJCSIs5+TkiFrLli11wrKpqakBOyW6vaKiIqxZswayLCMuLg7FxcWi5unpCbVaDbVajUGDBjFEExE1YgzORER031RUVGDz5s2QZRlRUVG4evWqqDk5OYmw7Ovry7BMjU5xcTHWrl0LWZYRGxuLoqIiUWvTpo2YiR40aBCMjIwM2CkREdUWgzMREdWr8vJynbB87do1UXN2dsaUKVMgSRJGjRoFExMTA3ZKVHeKi4uxbt06aDQaxMTEoLCwUNQ8PDwQFhYGSZIwZMgQhmgiokaAwZmIiOpceXk5Nm7cCFmWER0djdzcXFFzcXERYXnkyJEMy9TklZSUYP369ZBlGTExMSgoKBA1d3d3hIWFQa1WY9iwYQzRREQNFIMzERHVibKyMmzYsAGyLGP16tXIy8sTNVdXVzHDNmLECBgbGxuwUyLDKS0t1fl/kp+fL2qtW7cW/0+GDRvG/ydERA0IgzMREd01hgCiu3fzL5uio6N1/v+0atVKrMzgL5uIiAyPwZmIiGpF37JTNzc3nbDMZadENVNWVoZNmzbd8uMNrq6uOiGaH28gIrr/GJyJiOiOSkpKsHbt2lte6Mjd3V1cLZgXOiK6d7ygHhFRw8PgTEREt1STW+uo1WoMHjyYYZmonpSXlyM+Pv6Ot3AbPXo0QzQRUT1icCYiIqGoqAhr1qyBRqNBbGwsiouLRa1t27ZiZnngwIEMy0T3WUVFBRISEiDLMiIjI5GTkyNqjo6OOiGa90EnIqpbDM5ERM1cYWEh1qxZA1mWsWbNGp2w7OnpCUmSIEkSBgwYAJVKZcBOieiGiooKbN26FbIsIyIiAtnZ2aLWsmVLTJo0CZIkYezYsQzRRER1gMGZiKgZKiwsRGxsLGRZxtq1a1FSUiJq7du3hyRJUKvV6N+/P8MyUQNXWVmpE6KzsrJErUWLFggNDYUkSRg3bhzMzMwM2CkRUePF4ExE1EwUFBQgJiYGGo0Ga9euRWlpqah5eXmJmeW+ffsyLBM1UlVVVdi2bZsI0RkZGaLm4OCgE6LNzc0N2CkRUePC4ExE1ITl5+cjJiYGsixj3bp1KCsrE7WOHTuKsNy7d2+GZaImpqqqCtu3b4csywgPD0d6erqo2dvbIyQkBJIkYcKECQzRRER3wOBMRNTE5OXlYfXq1ZBlGevXr0d5ebmode7cWSzD7tWrF8MyUTNRVVWFpKQkEaKvXLkianZ2dggJCYFarcbEiRNhYWFhwE6JiBomBmcioiYgNzcX0dHR0Gg02LBhg05Y7tKli5hZ9vHxYVgmaua0Wi3+/vtvyLIMjUaDtLQ0UbO1tUVwcDAkScLEiRNhaWlpwE6JiBoOBmciokbq2rVriI6OhizL2LhxIyoqKkTN29tbhOXu3bszLBPRLWm1WuzYsQMajQYajQaXLl0SNRsbGwQFBUGSJPj7+zNEE1GzxuBMRNSIXL16FVFRUZBlGZs2bUJlZaWode/eXSzD7t69uwG7JKLGSKvVIjk5WcxEX7x4UdSsra0RFBQEtVqNgIAAWFlZGbBTIqL7j8GZiKiBy8nJQWRkJDQaDTZv3qwTlnv06CFmlr29vQ3YJRE1JYqiYNeuXSJEnz9/XtSsrKwQGBgISZIQEBAAa2trA3ZKRHR/MDgTETVA2dnZiIyMhCzLiI+PR1VVlaj17NlTzCx37drVgF0SUXOgKAp2794NjUYDWZZx7tw5UbO0tERAQAAkSUJgYCBsbGwM1ygRUT1icCYiaiAyMzNFWN6yZYtOWO7du7cIy507dzZgl0TUnCmKgr1790KWZciyjLNnz4qahYUFAgICoFarERQUBFtbWwN2SkRUtxiciYgMKCMjAxEREdBoNNiyZQu0Wq2o9enTR4TlTp06GbBLIqLqFEXB/v37RYhOTU0VNQsLC/j5+UGSJAQHBzNEE1Gjx+BMRHSfpaenIyIiArIsY9u2bTphuV+/fiIsd+jQwYBdEhHVnKIoOHDggFjOferUKVEzNzeHn58f1Go1QkJCeP5GRI0SgzMR0X1w5coVhIeHQ5ZlJCYm4ua30wEDBkCSJISFhcHLy8uAXRIR3TtFUXDo0CExE33y5ElRMzMzw8SJE8VMtIODg+EaJSKqBQZnIqJ6cvnyZYSHh0Oj0WD79u06YXngwIFiZrldu3aGa5KIqB4pioIjR46IEH38+HFRMzU1xYQJEyBJEkJDQxmiiahBY3AmIqpDly5dEjPLSUlJOrXBgweLmWVPT08DdUhEZBiKoiAlJUUs5z569KiomZqaYvz48VCr1Zg0aRJatGhhwE6JiKpjcCYiukcXL14UJ4I7duzQqQ0dOlSE5TZt2hioQyKihufo0aNiJjolJUVsNzExwbhx4yBJEiZNmoSWLVsasEsiousYnImI7sL58+fFzPLOnTt1asOGDRNh2cPDw0AdEhE1HseOHRO/gDx8+LDYbmJigjFjxogQ7eTkZMAuiag5Y3AmIqqhc+fOiRO7Xbt2ie0qlQrDhw+HJEmYMmUK3N3dDdglEVHjduLECfFee/DgQbHd2NgYY8aMgVqtxuTJk+Hs7GzALomouWFwJiLS4+zZs2Ip4Z49e8R2lUqFkSNHQq1WY8qUKXBzczNgl0RETdPJkydFiD5w4IDYbmxsDF9fX0iShMmTJ8PFxcVwTRJRs8DgTET0D6mpqeJEbe/evWK7kZERRo4cKWaWW7VqZcAuiYial9OnT4v35n379ontRkZGGDVqlHhvdnV1NWCXRNRUMTgTEeH6CdmNmeX9+/eL7UZGRjqzGjwhIyIyvNTUVHGdiZtXA934BadarUZYWBh/wUlEdYbBmYiarZMnT4qw/M/P0Y0ePVp8jo5LAImIGq6zZ8+Kmejdu3eL7SqVCiNGjBAXa2zdurUBuySixo7BmYialePHj4sTrEOHDontNy46c+PKrbzoDBFR43P+/HnxHp+cnCy2q1QqnTse8CKORFRbDM5E1OQdO3ZMzCwfOXJEbDcxMcHYsWNFWHZ0dDRgl0REVJcuXLgglnPv2LFDpzZs2DCo1Wqo1WreNpCIaoTBmYiapJSUFBGWjx49KrabmJhg/PjxUKvVmDRpElq2bGnALomI6H64ePGiCNF///23Tm3IkCGQJAlqtRpt2rQxUIdE1NAxOBNRk6Aoik5YPnbsmKiZmppi/PjxkCQJoaGhaNGihQE7JSIiQ7p8+bII0UlJSbj59HbQoEEiRHt6ehqwSyJqaBiciajRUhQFhw8fhizL0Gg0OH78uKiZmZlhwoQJkCQJISEhcHBwMFyjRETUIKWlpSE8PBwajQaJiYk6IXrgwIEiRLdr185wTRJRg8DgTESNiqIoOHjwoLj4y8mTJ0XNzMwMfn5+UKvVCAkJgb29vQE7JSKixuTKlSuIiIiALMvYtm2bToju37+/CNFeXl4G7JKIDKXOg/OUKVNq/OARERE13vcGBmei5kdRFBw4cEAswz59+rSomZubw8/PD5IkITg4mO8LRER0z9LT0xEZGQlZlrF161ZotVpR69u3LyRJgiRJ6NChgwG7JKL7qc6D8xNPPFHjB1+xYkWN972BwZmoeVAUBfv27RPLsFNTU0XNwsIC/v7+kCQJgYGBfC8gIqJ6k5GRgcjISGg0GiQkJOiE6D59+oiZ6E6dOhmwSyKqb1yqTUQNhqIo2LNnDzQaDTQaDc6cOSNqlpaWCAgIgFqtRmBgIGxtbQ3YKRERNUdZWVliJjohIQFVVVWi1qtXLzET3blzZwN2SUT1od6Dc2VlJbZs2YLU1FQ89NBDsLW1RVpaGuzs7GBjY1OvDRNRw6coCnbv3i1mls+dOydqlpaWCAwMhCRJCAgIuKv3DCIiovqQnZ0tZqI3b96sE6J9fHxEiO7atasBuySiulKvwfn8+fPw8/PDhQsXUFZWhpMnT8LLywsvvvgiSktLsWzZsnptmIgaJkVRkJycLMLyhQsXRM3KygpBQUGQJAn+/v6wtrY2YKdERER3lpOTg6ioKMiyjM2bN6OyslLUevToIZZzd+vWzYBdEtG9qNfgPGnSJNja2mL58uVwdHTEwYMH4eXlha1bt+Kpp57CqVOn6rVhImo4tFotdu7cKZZhX7x4UdSsra0RHBwMtVoNf39/WFlZGbBTIiKiu3f16lVER0dDlmVs3LhRJ0R369ZNzER3797dgF0SUW3Va3B2cnJCUlISunTpAltbWxGcz507h27duqG4uLheGyYiw9JqtdixYwdkWUZ4eDguXbokajY2NggODoYkSfDz84OlpaUBOyUiIqp7165dQ3R0NDQaDTZs2ICKigpR8/b2hlqthiRJ6NGjB1QqlQE7JaI7qdfg3LJlS2zfvh3dunXTCc7bt29HWFgYMjIy6rVhIrr/tFotkpKSRFhOS0sTNVtbW4SEhECSJEyYMIFhmYiImo3c3FysXr0asixjw4YNKC8vF7UuXbqI5dw9e/ZkiCZqgOo1OE+dOhX29vb44YcfYGtri0OHDsHZ2RmhoaFo27Ytb0dF1ERUVVXphOUrV66Imp2dHUJDQ6FWqzFhwgRYWFgYsFMiIiLDy8vLQ0xMDGRZxrp163RCdKdOncRy7l69ejFEEzUQ9Rqc09LSMHr0aBgbG+PUqVPo378/Tp06BScnJ2zbtg0uLi712jAR1Z+qqiokJiZClmVEREQgPT1d1Ozt7REaGgpJkjB+/HiYm5sbsFMiIqKGKz8/HzExMdBoNFi7di3KyspErWPHjmI5d58+fRiiiQyo3m9HVVJSglWrVmHfvn3QarXo27cvpk+fftdLNBmciQynsrIS27ZtE2E5MzNT1BwcHDBp0iRIkoSxY8cyLBMREdVSQUEBYmNjIcsy1q5di9LSUlHz8vISy7n79evHEE10n9VrcC4uLq7zq+MyODc/iqLo3BuxOVCpVDA2NjZ0GwCuh+WtW7eKsJyVlSVqLVq00AnLZmZmBuyUiIio6SgsLERcXBxkWcaaNWtQUlIiau3btxcz0f37928QIZrna9TU1WtwtrGxwaRJk/DII49g/PjxMDIyuqdmAQbn5uDmJcAxMbHIyEjX+exPc2FpaYk2bdpiypTJ932JVmVlJRISEiDLMiIjI5GdnS1qLVu2xOTJ13saM2YMTE1N70tPREREzVVhYSHWrFkDjUaDuLg4nTvTeHp6ihA9cODA+3auwPO16wx5vkb3V70G54iICKxatQpxcXGws7PD1KlT8fDDD2PAgAH3pWFqfPLy8jBxoh+Sk3fCubU7Bo73R6u27WBhZd2s3oQUrRbFRYW4cPIYdm9ah/zca5j24IP4z6+/wsTEpF4es6KiAvHx8ZBlGVFRUcjJyRE1R0dHTJkyBZIkwdfXl2GZiIjIQIqKirB27VrIsozY2FidEN22bVuo1Wqo1WoMGjSoTiatboXna9cZ4nyNDKfeP+MMXP+8hkajwapVq5CQkID27dvj4Ycfxvz58+u1YWpcbrwJpxw7hjlffg+fwcPr7Q2/MamsqEBibCSWvv0K1Go1fvvPf+rszbi8vFwnLF+9elXUnJycdMIyfwAQERE1LMXFxVi3bt1/Z31jUFRUJGoeHh5iJnrw4MF1dk7F87Vbq8/zNWoY7ktwvtnRo0cxffp0HDp06K4+B8Hg3HTNnz8fiz/7HAv+rUFHn16GbqfB2bE+Dotf+BdWrVqFadOm3fU45eXl2LRpE2RZRnR0NK5duyZqLi4uIiyPHDmSb/hERESNRElJCdatWweNRoPVq1ejsLBQ1Nzd3REWFgZJkjB06NB7Cro8X9Ovrs7XqOG5L8G5tLQUq1evxu+//45169bBxcUFDz74ID7++ON6bZgaD0VR0LWrN9y69cKsj740dDsN1lzJHz6dOiAiPLxWx5WVlWHjxo0iLOfl5Ymaq6ur+GE6YsQIXuSCiIiokSstLcX69eshyzJWr16NgoICUXNzc9MJ0bX5uc/ztZq52/M1atjqNThv2LABK1euRFRUFIyNjaFWqzF9+nSMGjXqvjRMjceRI0fg4+ODed//B/1GjTV0Ow1W1E/fQf72M2RlZcHGxkbvvqWlpSIsr169Wicst2rVSvzQHD58OMMyERFRE3Xz+UB0dDTy8/NFrbbnAzxfq5nanK9R41GbHFrrNZuTJk1CYGAg/v3vfyMwMJAXFKLbSklJAQB07dPfwJ00bF37DkRpaSnOnTuHHj16VKvX12+YiYiIqHGysLBAcHAwgoODq61AS09Px3fffYfvvvsOrq6uOh/XutV5As/XauZO52vU9NU6OKenp3NWmGokNzcXKpUKlja2hm6lQbOxdwBw/fW64ebPNMXExOiEZXd3d3F1zXv9TBMRERE1bubm5ggKCkJQUJDONU+ioqKQkZGBpUuXYunSpbe95gnP12rmVudr1LzUOjjb2dkhNTUVK1asQGpqKr766iu4uLhg3bp1aNOmDbp3714ffVIjpNVqYWRszGB3B0b//e1vcXExIiIixK0obr4ASH1dRZOIiIiaDjMzMwQEBCAgIADff/+9uMtGZGQkMjMzsWzZMixbtgzOzs6YPPn6PYorKip4vlYDN87XtFqtgTshQ6l1cN66dSv8/f0xbNgwbNu2DR988AFcXFxw6NAh/PTTT9BoNPXRJzVheTnZWPXVJ9ifGI/c7GzY2NvDs0s3TH3+ZXS5i2VDYV3dqm17esFHmDjtUfH1+RPH8NN7b+L04QOwsXfA+KkPQ3ruJb33KSzMy8XyD97GnvgNAID+Yybgqbfeh7WdvdgnK+0Sflw4D0eSk2BmboERQZPx6GvzYWpmdse+Q0NDUVpaKr6+cd9GSZIwcOBA/kAjIiKiGjMzM4Ofnx/8/PywbNkynRCdlZWFH374AT/88AOsra1Rk0se8XyNmrtaB+fXX38d77//PubMmQNb2/8t6Rg9ejS++uqrOm2OmodPZz+FyspKPL/oK7i28UReThYO79iOwrzcux5z5odfoM+I0eJrq5u+V4sLC7Dw/6ah+8Ch+Fheg7RzZ/DtGy/CwtIKIU8+c9sxv3xlJnLSr+CtH1cCAJbNfw1fvTYL85b9CgCoqqrChzMehV1LR7y/MgoFudfw7esvQlEUPPX2B3fsubS0FJ6enpAkCWq1GgMHDtT7g4GIiIioJkxNTTFx4kRMnDgRS5cuxZYtW0SIzs7OhpHRna+RwvM1au5qHZwPHz6M33//vdp2Z2dn5OTk1ElT1HwU5efh2N5dWPhrOLoPHAIAcHH3QKeefe5pXGs7O7RwdrllbVtMBMrLyjDroy9hamaOtp27Iu1cKmJ++QHBT8y4ZVi9lHoK+xMTsOjPWHTu1RcA8Ox7n+KNacG4fOY03L064mDSVlxKPYnvf9qDlq6tAACPzZ2Pb994CQ+99Dqs7vDZoWXLluHpp59mWCYiIqJ6Y2pqivHjx2P8+PFYsmQJXn75ZXz73Xd6j+H5GtFdBGcHBwdcuXIF7du319m+f/9+uLu711lj1DxYWFnDwsoauzavQ+fefWFqZl5tn/f/NR3H9ibrHWflvtM6X//03ltY+tYrcPFoi7HqBzH+gYfFUueTB/ai+4DBOo/Ve7gvVn6+CJmXL8LVo2218U8c2AMrWzvxJgwAnXv3g5WtHU7s3wN3r444cWAP2nTqKt6Eb4xbUV6G1COH4DN4mN7n4O3tzdBMRERE942JiQm6du16x/MPnq8R3UVwfuihhzB37lzIsgyVSgWtVoukpCS88sorePTRR+88ANFNjE1M8PyiL7Fs/qvY8Md/0L5bD3QfMATDAkPRrks3AMCz7y9G+U2f/b2TB194DT6Dh8PMwgKHd2zHvz9+FwXXrkL97IsAgNysTDi7t9E5xsHRWdRu9Uacm5UF+5ZO1bbbt3RCbnaW2MfBUXcfG3sHmJiaITc7s8b9ExERETUkPF8juovg/MEHH+Dxxx+Hu7s7FEVBt27dUFVVhYceeghvvvlmffRITdyQiYHo5zsWx/Yk48SBvTiQmICo5Uvw7HuLMWbKVDi6tq7VeDfecAGgvff1++zJS77Q2f7P36wqUG65/Wa3KilQANUddoLCmWQiIiJq1Hi+Rs1drYOzqakpVq5ciffeew/79u2DVqtFnz590KlTp/roj5oJM3ML9Bo2Cr2GjcIDM+dgyVsv489vr78R383Sn5t17t0XxYUFyM3OgoOTMxycXar9RjEvJxsAYO/kfMsxHJydkfvffW6WfzVH/PbTwdkZpw7t16kX5uWisqIC9o63HpeIiIioseD5GjVntQ7ON3h5ecHLy0t8ffDgQfTt2xdVVVV10hg1bx4dOmPXpnUAar/055/OHD0CM3MLWNvZAbj+WZffv/gIFeXl4rYDB5O2oqVLK7j8Y0nQDV1690dxQT5OHdovLoRx8uA+FBfki1swdOndHxHLvsa1zAy0cHEV45qamaNDj5533T8RERFRQ8TzNWpO7jo430pN7gFHdLOCa1ex+MUZGBM2DZ5dvGFpbYPUIwcRvXwJBoydCAC1WvqzO34DcrOz0KV3P5hZWOBIchJWffkxxj0wXVxcYkTQZMjffY5v33gRYTNm48r5s4j4/hud+wKeOrQfX8+djQW//AVH19bw6NAJfUaMxtK3X8Uz734MAFg6/zX08x0Hd6+OAIBew0bBo0NnfDV3Fh599W0U5uXi358sxDjpIV6hkYiIiBotnq8R1XFw5ucCqLYsrK3RqWcfxP7yA9IvnkdVZQUcW7lhnDQdU2bMqvV4JqamWL/qF/zy0QIoihauHp6YOvtV+D/0uNjH2tYO85f/gR/fm4fX1P6wtrdH8ONPI/iJGWKfspISpJ1NRVVFpdj2wqff4ucP3sbC/3sQADBgzASd+/0ZGxtj3ve/4sd35+HNh0JhZm6JEUGT8Njc+XfxyhARERE1DDxfIwJUSh1NE9/LUu38/HzY29sjLy8Pdv9dnkGN39KlSzFr9mz8deSCoVtp0NLOncEsv+HYunUrRo4caeh2iIiIqBnh+VrN8HytaapNDq3xjHN+fr7eekFBQU2HIiIiIiIiImo0ahycHRwc9C7FVhRewp2IiIiIiIianhoH54SEhPrsg4iIiIiIiKhBqnFwHjVqVH32QURERERERNQgGRm6ASIiIiIiIqKGjMGZGowPn3kUC5544Ja1E/v3IKyrG86kHKr1uBXlZVj5xUeYMWYApvq0w3Pjh2Bz+Krb7n/ueAo+n/Msnvbthwd7eWF2wEjE/vqTzj6Zly4irKtbtT/7E/mRBiIiImq66uN8beeGNXj3yal4YkgPPNyvM96YGoz9iVvueFxW2iV8+MyjeKhPBzw+uDuWv/8WKsrLdfY5f+IY3n54Ch7s5YV/jeyLv777HHV0UyFqZur0Ps5E92Ks+kF8OuspZF6+BBd3D51afMQfaO/dHV7de9Z63M9enIHcnGw89/5naN22PfKuZqOqsvK2+6emHIJ9S0e88Mm3cGzthhP792DZ/FdhZGSEgIef1Nn3nRV/ok3HLuJrG3uHWvdHRERE1FjUx/na0T070WvoSEx/6Q1Y2dohIeJPfPTcY1j0Zyy8uvnc8piqqip8OONR2LV0xPsro1CQew3fvv4iFEUR920uLizAwv+bhu4Dh+JjeQ3Szp3Bt2+8CAtLK4Q8+czdvQDUbDE4U4PR33c87B2dsCXyTzzw/Mtie1lJMZLWrMZDL71e6zH3JyYgZfdOLNm4A7YOLQAALh5t9B4zNuxBna9btfHEyQN7kLxxbbXgbOvQAi2cXWrdFxEREVFjVB/na0/OW6jz9fQ5b2BX/HrsSdh42+B8MGkrLqWexPc/7UFL11YAgMfmzse3b7yEh156HVY2ttgWE4HysjLM+uhLmJqZo23nrkg7l4qYX35A8BMzeEcgqpW7Ds6nT59GamoqRo4cCUtLS96Oiu6ZsYkJRoWqkRD5F6SZc8T309/rYlFZUYGRwVMAANP7dtQ7jne/QXjrx5UAgN3xG9ChR09ELV+CbdHhMLe0woAx4zHthddgbmFZ496KCwpuOZv80XOPo7ysDK092yP4sacxxC+oxmMSERERNTb1cb72T1qtFqVFhXpX8p04sAdtOnUVoRkAeg/3RUV5GVKPHILP4GE4eWAvug8YDFMzc519Vn6+CJmXL8LVo21NnzZR7YNzTk4Opk6divj4eKhUKpw6dQpeXl546qmn4ODggM8++6w++qRmYkzYNEQvX4ojyX/DZ/AwAEB8+B8YNN5fvHkujtyodwwzCwvx94yL53F8726YmVngtW+XI//aVfz47hsozMvFzA+/qFFPJ/bvwd/rYjBv2a9im4W1FR5/fQG69h0AlcoIuxPW4/M5z+D58q8wKiSsls+aiIiIqPGo6/O1f1q9YhlKi0swzD/ktvvkZmXBwdFJZ5uNvQNMTM2Qm535330y4eyuu9LQwdFZ1BicqTZqHZxfeuklmJiY4MKFC/D29hbbp06dipdeeonBme6Jh1cndOnTH/ERf8Bn8DCkXziHY3uT8fby/13Mq7Vn+xqPp2i1UKlUeGHxt7C2tQMAVLy+AItf+Beemv/hHWedL5w6gY9mPgHpuZfQa9j/bslm18IRwY8/Lb7u6NMLRXl5iPppCYMzERERNWl1fb52s8TYSPz17WeY+90K2P8jGFdzy9Wuuqtg/7kiVoFyy+1Ed1Lr4LxhwwasX78eHh66FwPo1KkTzp8/X2eNUfM1Vv0gfnrvTfxr/oeIj/gTzm4e6DlkhKjXZulPC2dXtHRtJUIzAHh06ARFUZCTfgVu7bxuO87F0yex4HEJ46TpUD/74h377ty7HzZrbn+1biIiIqKmoi7P125IWhONJW+9jFe+/AG9ho7Ue7yDszNOHdqvs60wLxeVFRWw/++ssoOzi5h9viEvJxsAYO/krP8JEv1DrYNzUVERrKysqm3Pzs6Gubn5LY4gqp2hfiH4+YP5SIyNxJaovzBOmq7zW8HaLP3p0ncA/l4fg5KiIlhaWwMA0s6lwsjICI6tWt92jAunTmDB4xJ8J0mYXsOLXJw9ehgOvFAYERERNQN1eb4GXJ9pXvLmy3jxs+/Qz3fcHR+/S+/+iFj2Na5lZqCFiyuA6xcMMzUzR4ce16/q3bl3P/z+xUeoKC+HqZmZ2KelSyu4uOu/WCzRP9X6Ps4jR47Er7/+77OeKpUKWq0Wn376KUaPHl2nzVHzZGltjWEBIfj9i49wLTMDoyfr3iuwtWd7vX8cXf8XiEcETYatQwt8N+8lXDx9Eim7d+LXT97HmLBpYpl28sa1mOX/v9+QXjh1Au88pkavoSMR/PgMXMvKxLWsTORdzRH7JET+hcSYCFxKPYXLZ04jevlSrPnt52pX3SYiIiJqiuryfC0xNhLfvP4CHps7H5179RPnXkUF+WKff56v9Ro2Ch4dOuOrubNw5uhhHNqRiH9/shDjpIdgZWML4Pp5oKmZGb5940VcOHkcyRvXIuL7bxD8+NNcqk21VusZ508//RS+vr7Ys2cPysvL8dprryElJQVXr15FUlJSffRIzdDYsAexWbMKvYaNgrObx50PuA1La2vM//kPLH//Lbym9oOtQwsM9QvBgy++JvYpKshH2tlU8fWOdTHIv5qDbTER2BYTIbY7u3lgWfwu8bVm2VfISrsEIyNjuLXzwnMffH5Pn2+eOXMmnnrqKYSFhVX7KAQRERFRXTp27Bg0Gg2WLVsGRavc1Rh1db628c/fUFVZiR8XzsOPC+eJ7b6THsCsj74EUP18zdjYGPO+/xU/vjsPbz4UCjNzS4wImoTH5s4X+1jb2mH+8j/w43vz8JraH9b29gh+/GkEPzHjrnul5kulKEqt/6ekp6dj6dKl2Lt3L7RaLfr27YuZM2eidevbL33VJz8/H/b29sjLy4Odnd2dD6BGYenSpZg1ezb+OnLB0K00aGnnzmCW33CdbUOGDIEkSVCr1WjThkuJiIiI6N4dPXoUsixDlmWkpKSI7UbGxpBTLhqws4bvxvna1q1bMXKk/s9fU+NRmxx6V/dxbtWqFd599927ao6Ibm3WrFnYv38/kpKSsGPHDuzYsQNz5szB4MGDIUkSwsLC4Onpaeg2iYiIqJFQFAUpKSkiLB87dkzUTE1NMX78eDg6OuL3Vby4KdGd1PozzitWrIAsy9W2y7KMf//733XSFDUhtV/Q0Pz89zVSq9VITEzEpUuX8PXXX2PEiBFQqVTYuXMnXn75ZbRr1w6DBg3C4sWLce7cOcP2TERERA2Soig4dOgQ5s+fj27dusHHxwcLFy7EsWPHYGZmhqCgIPzyyy/IyMhAXFwchgwZwvO1muBr1OzVOjh/9NFHcHKqfk81FxcXfPjhh3XSFDUNVlZWqKqqQkV5maFbadBKi4sAANb/veq3m5sbZs2ahW3btuHy5cv49ttvMWrUKKhUKuzatQuvvvoq2rdvjwEDBuCTTz7B2bNnDdk+ERERGZiiKDh48CDeeustdO3aFb169cJ7772H48ePw8zMDMHBwfj111+RmZmJmJgYPPbYY2jRogUAnq/V1D/P16j5qfVS7fPnz6N9++o3NPf09MSFC/wsK/1Pq1atAAAZly7Aw6uTgbtpuDIuXf9MkYtL9VtZtW7dGjNnzsTMmTORnp6OiIgIaDQabN26FXv27MGePXswd+5c9OvXT3wmukOHDvf7KRAREdF9pigKDhw4AFmWodFocOrUKVEzNzeHn58fJElCUFAQ7O3tbzsOz9dqRt/5GjUPtZ5xdnFxwaFDh6ptP3jwIBwdHeukKWoaRowYAUsrKyRvWGvoVhq05I1r0L17jzteBKxVq1Z47rnnEB8fj7S0NCxduhRjxoyBkZER9u7di9dffx0dO3ZE3759sWjRIpw+ffo+PQMiIiK6HxRFwd69e/HGG2+gU6dO4mf+qVOnYGFhgcmTJ2PlypXIzMxEVFQUpk+frjc0Azxfq6manq9R01Xr4Dxt2jTMnj0bCQkJqKqqQlVVFeLj4/HCCy9g2rRp9dEjNVJWVlYICQ5G0pooVFZUGLqdBqkwLxd7t2zE1KkP3Hnnm7i6uuKZZ57B5s2bkZ6eju+//x7jxo2DsbEx9u/fj3nz5qFTp07o3bs3PvjgA5w8ebKengERERHVJ0VRxAqzjh07on///vjoo4+QmpoKCwsLTJkyBatWrUJmZiYiIiLw0EMP1eouNTxfu7O7PV+jpqXWt6MqLy/HI488AlmWYWJyfaW3VqvFo48+imXLlsHMzKzWTfB2VE1XYmIixo4di36jJ+Clz5bAxNTU0C01GIV5uXjv/x5ETtpF7Nu7F+3atbvnMbOzsxEZGQmNRoPNmzejqqpK1Hr27CmWc3ft2vWeH4uIiIjqh6Io2L17t1iGffNFQS0tLREYGAhJkhAQEAAbG5t7fjyer91efZyvUcNRmxx6V/dxBoCTJ0/i4MGDsLS0hI+Pzz3dJofBuWlbvXr19fsRd+qCkSFqDJ4QAKfW7lCpVIZu7b5TFAUXT5/EjnUx2LZag7KiQsRv3ozevXvX+WPl5OQgKioKsixj8+bNqKysFLUePXpAkiRIkgRvb+86f2wiIiKqHUVRkJycDI1GA41Gg/Pnz4ualZUVgoKCoFarERAQUC8XqOL52v/cz/M1Mqz7EpzrEoNz0xcfH48vv/oK69etQ3l5OYxNTGBpZd2s3oy1ihYlhYXQarWwtbPDpNBQvPbaa+jRo0e9P/bVq1cRHR0NWZaxceNGnRDdrVs3EaK7d+9e770QERHRdVqtFsnJyWJm+eLFi6JmbW2NoKAgSJIEf39/WFlZ1Xs/PF8z7Pka3X91HpznzJmD9957D9bW1pgzZ47efT///PPadQsG5+YkPz8fmzZtQnp6OgoLCw3dzn2lUqlgZ2eHtm3bYsyYMTA3NzdIH9euXUN0dDQ0Gg02bNiAips+z+Tt7S2Wc/fo0aNZ/aAkIiK6H7RaLXbs2AFZlhEeHo5Lly6Jmo2NDYKDgyFJEvz8/GBpaWmQHnm+ZvjzNbo/6jw4jx49GpGRkXBwcICvr+9tT6ZVKhXi4+PrtWEiqju5ublYvXo1ZFnGhg0bUF5eLmpdunQRM9E+Pj4M0URERHdJq9UiKSkJGo0G4eHhuHz5sqjZ2toiJCQEarUaEydONFhYJmqOuFSbiGotLy8PMTExkGUZ6/67ROuGzp07Q61WQ5Ik9OrViyGaiIjoDqqqqpCUlCRmlq9cuSJqdnZ2CAkJgSRJmDBhAiwsLAzYKVHzVW/BubKyEhYWFjhw4ECdrvNncCZqWPLz8xETEwONRoO1a9eirKxM1Dp27CiWc/fp04chmoiI6L+qqqqQmJgIWZYRERGB9PR0UbO3t0doaCgkScL48eO5BJioAajXGecOHTogIiICvXr1uqcmb8bgTNRwFRQUIDY2FrIsY+3atSgtLRW1Dh06iJnovn37MkQTEVGzU1lZqROWMzIyRM3BwUGE5XHjxjEsEzUw9RqcV6xYAVmW8dtvv6Fly5b31OgNDM5EjUNhYSHi4uIgyzLWrFmDkpISUWvfvr0I0f3792eIJiKiJquyshJbt24VYTkrK0vUWrRogUmTJkGSJIwdOxZmZmYG7JSI9KnX4NynTx+cPn0aFRUV8PT0rHYfuX379tVrw0TUMBQWFmLNmjXQaDSIi4tDcXGxqLVr1w5qtRpqtRoDBw5kiCYiokavsrISCQkJkGUZkZGRyM7OFrWWLVti8uTJkCQJY8aMgampqQE7JaKaqtfgvGDBAr0nwe+8805thgPA4EzU2BUVFWHt2rWQZRmxsbE6Ibpt27ZiJnrQoEEM0URE1GhUVFTohOWcnBxRc3R0FGF59OjRDMtEjRCvqk1EBlNcXIx169ZBlmXExMSgqKhI1Nq0aYOwsDBIkoTBgwfDyMjIgJ0SERFVV1FRgc2bN0OWZURFReHq1aui5uTkhClTpkCSJPj6+sLExMSAnRLRvaqX4FxcXIxXX30VUVFRqKiowLhx4/D111/DycnpvjZMRI1HSUmJToguLCwUNXd3d7Gce+jQoQzRRERkMOXl5di0aRNkWUZ0dDSuXbsmai4uLiIsjxw5kmGZqAmpl+D86quvYsmSJZg+fTosLCywatUq+Pr6Qpbl+9owETVOJSUl2LBhA2RZxurVq1FQUCBqbm5uYiZ62LBhDNFERFTvysrKdMJybm6uqLm6uuqEZWNjY8M1SkT1pl6Cc4cOHfDBBx9g2rRpAIBdu3Zh2LBhKC0tvec3EwZnoualtLQUGzZsgEajQXR0NPLz80WtdevW4mRl+PDhPFkhIqI6U1ZWpvNL3Ly8PFFr1aqV+CUuf/4QNQ/1EpzNzMxw9uxZuLu7i22WlpY4efIk2rRpc98aJqKmpaysDBs3bhS/8f/nScyNED1ixAiexBARUa2VlpZi/fr10Gg0WL16dbVf1t64gOXQoUP5c4aomamX4GxsbIz09HQ4OzuLbba2tjh06BDat29/3xomoqarrKxM54IsNy+b42fMiIiopkpKSrB+/XpxjY2bPx7k7u4uZpZ5jQ2i5q1egrORkRH8/f1hbm4utsXExGDMmDE693KOiIio14aJqHkoLy/XCdE3X6jF2dlZ3AKEVzUlIiLgeli++daIN1+Q0sPDQ8ws864ORHRDvQTnJ554okYPvmLFihrtdzMGZyLSp6KiAvHx8eI+mv+8NcjNIZr30SQiaj6Ki4uxZs0aaDQaxMbG6twCsW3btuLuDYMGDWJYJqJqeB9nImqyKioqsGXLFsiyjIiICOTk5Iiao6MjJk2aBEmSMGbMGIZoIqImqKioCGvWrIEsy4iLi0NxcbGoeXp6ipnlgQMHQqVSGbBTImroGJyJqFmorKzUCdHZ2dmi1qJFCxGix44dCzMzMwN2SkRE96KwsBBxcXGQZRlr1qxBSUmJqLVr1w6SJEGSJPTv359hmYhqjMGZiJqdyspKbNu2TYTozMxMUXNwcBAhety4cQzRRESNQEFBAWJjY6HRaLBmzRqUlpaKmpeXFyRJglqtRr9+/RiWieiuMDgTUbNWVVWFxMREyLKM8PBwZGRkiJq9vT1CQ0MhSRLGjx+vc8FDIiIyrPz8fMTGxkKWZaxbt04nLHfo0EHMLPfp04dhmYjuGYMzEdF/VVVVYfv27SJEp6eni5qdnR1CQkIgSRImTJgACwsLA3ZKRNQ85eXlISYmBrIsY/369SgrKxO1Tp06ibDcq1cvhmUiqlMMzkREt1BVVYW///5bhOi0tDRRs7W1FSF64sSJDNFERPUoNzcXq1evhkajwfr161FeXi5qnTt3FmG5Z8+eDMtEVG8YnImI7kCr1eLvv/+GRqOBRqPB5cuXRc3GxgbBwcGQJAl+fn6wtLQ0YKdERE1Dbm4uoqOjIcsyNmzYgIqKClHr2rWrCMs9evRgWCai+4LBmYioFrRaLXbu3AlZlqHRaHDp0iVRs7GxQVBQENRqNfz9/WFlZWXATomIGperV6+KsLxp0yadsNytWzdxga/u3bszLBPRfcfgTER0l7RaLXbt2iVC9IULF0TN2toagYGBkCQJ/v7+sLa2NmCnREQNU05ODqKioqDRaLBp0yZUVlaKWvfu3cXMcrdu3QzYJRERgzMRUZ1QFAW7du2CRqOBLMs4f/68qFlZWSEgIACSJCEwMJAhmoiatezsbERFRUGWZcTHx+uEZR8fHzGz7O3tbcAuiYh0MTgTEdUxRVGwZ88eyLIMWZZx7tw5UbO0tERAQADUajWCgoJgY2NjuEaJiO6TrKwsREZGQpZlJCQkoKqqStR69eolwnKXLl0M2CUR0e0xOBMR1SNFUbBv3z4Ros+cOSNqFhYW8Pf3hyRJCAoKgq2trQE7JSKqW5mZmYiIiIBGo8GWLVt0wnLv3r1FWO7cubMBuyQiqhkGZyKi+0RRFOzfv18s5z59+rSomZubw8/PD5IkITg4mO9vRNQoZWRkICIiArIsY+vWrdBqtaLWt29fEZY7duxowC6JiGqPwZmIyAAURcHBgwfFTPSpU6dEzdzcHBMnToRarUZISAjs7e0N2CkRkX7p6ekIDw+HLMvYtm0bbj5d7N+/PyRJQlhYGDp06GDALomI7g2DMxGRgSmKgsOHD4sQfeLECVEzMzPDhAkTIEkSQkJC4ODgYLhGiYj+Ky0tDeHh4dBoNEhMTNQJywMGDBAzy+3btzdgl0REdYfBmYioAVEUBUeOHBHLuY8dOyZqpqamGD9+PCRJQmhoKFq0aGHATomoubl8+bKYWU5KStIJy4MGDRJh2dPT04BdEhHVDwZnIqIGLCUlRcxEHz16VGw3NTXFuHHjoFarMWnSJLRs2dKAXRJRU3Xp0iXxi7y///5bpzZkyBCxDLtt27YG6pCI6P5gcCYiaiSOHj0qTmCPHDkitpuYmGDs2LGQJAmTJk2Co6OjAbskosbuwoULYmZ5x44dOrWhQ4eKsNymTRsDdUhEdP8xOBMRNULHjx8XIfrQoUNiu7GxMcaMGQNJkjB58mQ4OTkZsEsiaizOnz8v3lOSk5PFdpVKhWHDhomw7O7ubsAuiYgMh8GZiKiRO3nypFjOffDgQbHd2NgYo0ePhlqtxpQpU+Ds7GzALomooTl79qwIy7t37xbbVSoVRowYAbVajbCwMLi5uRmwSyKihoHBmYioCTl16pQ4Ed6/f7/YbmRkBF9fX0iShClTpsDFxcWAXRKRoZw5c0a8R+zZs0dsV6lUGDlypHiPaN26tQG7JCJqeBiciYiaqNOnT4sT5H379ontRkZGOifIrVq1MmCXRFTfUlNTxaqUf74XjBo1Sny0g+8FRES3x+BMRNQM3GmW6caSTM4yETUNp06dEmH5wIEDYruRkZH4CMfkyZPh6upquCaJiBoRBmciombm7Nmz4oq5u3btEttVKhWGDx8uLgLEzzUSNS4nTpwQvyC71fUObsws83oHRES1x+BMRNSM6buS7s23nfHw8DBgl0R0O8ePHxczy4cPHxbbjY2NdW5TxyvsExHdGwZnIiICwHu3EjUWR48eFWE5JSVFbDcxMcG4ceOgVqt5T3ciojrG4ExERNVcvHgRERERkGUZSUlJOrXBgwdDkiSo1Wq0bdvWQB0SNR+KoiAlJUWsDjl69KiomZqaYty4cZAkCaGhoWjZsqUBOyUiaroYnImISK/Lly+LmeikpCTc/KNg4MCBIkS3a9fOcE0SNTGKouDIkSNiZvn48eOiZmpqigkTJkCSJISEhKBFixYG7JSIqHlgcCYiohpLS0sTM9GJiYk6IXrAgAEiRLdv396AXRI1Toqi4NChQ5BlGRqNBidOnBA1MzMzTJw4EWq1GiEhIXBwcDBco0REzRCDMxER3ZUrV64gIiICGo0G27Ztg1arFbV+/fpBkiRIkgQvLy8DdknUsCmKggMHDohl2KdOnRI1c3NzTJw4EZIkITg4GPb29gbslIioeWNwJiKie5aRkSFmordu3aoTovv06SNCdMeOHQ3YJVHDoCgK9u/fL2aWT58+LWrm5ubw9/eHJEkICgriuQ4RUQPB4ExERHUqMzMTkZGRkGUZCQkJOiG6d+/eYjl3586dDdgl0f2lKAr27t0rwvKZM2dEzcLCAgEBAVCr1QgKCoKtra0BOyUiolthcCYionqTlZWFyMhIaDQaxMfHo6qqStR69uwpZqK7dOliwC6J6oeiKNi9ezc0Gg00Gg3Onj0rapaWlggICIAkSQgMDISNjY0BOyUiojthcCYiovsiOzsbUVFRkGUZmzdv1gnRPXr0ECHa29vbgF0S3RtFUbBr1y4xs3z+/HlRs7KyQmBgICRJQkBAAKytrQ3YKRER1QaDMxER3Xc5OTmIjo6GLMvYtGkTKisrRa179+5iOXf37t0N2CVRzWi1WiQnJ4uwfPHiRVGztrZGUFAQ1Go1/P39GZaJiBopBmciIjKoq1evIjo6GhqNBhs3bkRFRYWoeXt7i5no7t27Q6VSGbBTov/RarXYsWOHWIZ96dIlUbO2tkZwcDAkSYKfnx+srKwM2CkREdUFBmciImowrl27htWrV0OWZWzYsEEnRHft2hVqtRqSJMHHx4chmu47rVaLv//+G7IsIzw8HJcvXxY1GxsbhISEQJIkTJw4EZaWlgbslIiI6hqDMxERNUi5ubmIiYmBLMtYv349ysvLRa1z585iOXevXr0YoqneVFVVISkpSYTlK1euiJqdnR1CQkKgVqsxceJEWFhYGLBTIiKqTwzORETU4OXl5SEmJgYajQbr1q1DWVmZqHXs2FEs5+7duzdDNN2zqqoqbN++XYTl9PR0UbOzs0NoaCgkScKECRNgbm5uwE6JiOh+YXAmIqJGJT8/H7GxsZBlGWvXrtUJ0R06dBDLufv27csQTTVWVVWFbdu2QZZlREREICMjQ9Ts7e0xadIkSJKEcePGMSwTETVDDM5ERNRoFRQUIC4uDrIsY82aNSgtLRU1Ly8vqNVqqNVq9O/fnyGaqqmsrMTWrVshyzIiIyORmZkpag4ODjph2czMzICdEhGRoTE4ExFRk1BYWIi4uDhoNBrExcWhpKRE1Nq1aydmogcMGGCwEH3t2jXs27cPV69e1bnwWXNhYWEBJycnDBgwwGAXz6qsrMSWLVtEWM7KyhK1li1birA8ZswYhmUiIhIYnImIqMkpKirCmjVrIMsy4uLiUFxcLGpt27YVIXrQoEH1HqIVRcGqVavw228rsWnTxmYZmP/J2sYGIcHBePLJJzFu3Lh6f7yKigokJCSIsJyTkyNqjo6OmDx5MiRJwujRo2Fqalrv/RARUePD4ExERE1acXEx1q5dC1mWERsbi6KiIlFr06aNWM49ePBgGBkZ1eljK4qCuXPn4tNPP0W3fgMxeGIQeg/3hb2jE0yb4WxmeWkpcjLTsSd+A/5euxoXTp3ATz/9hCeffLLOH6uiogKbN2+GLMuIiorC1atXRc3JyUmEZV9fX4ZlIiK6IwZnIiJqNoqLi7Fu3TpoNBrExMSgsLBQ1Dw8PBAWFgZJkjBkyJA6CdHvvPMOFi5ciCfnLUTgo0/d83hNiVarxY8L52Hjn//BypUr8eCDD97zmOXl5Tph+dq1a6Lm7OyMKVOmQJIkjBo1CiYmJvf8eERE1HwwOBMRUbNUUlKC9evXQ5ZlxMTEoKCgQNTc3NxEiB42bNhdheji4mI4OTtj4kOP45FX3qrL1psMrVaLj557HCVZV5By5MhdjVFeXo6NGzdClmVER0cjNzdX1FxcXERYHjlyJMMyERHdNQZnIiJq9kpLS7FhwwbIsozVq1cjPz9f1Fq3bq0Too2NjWs0pkajgSRJ+G7D32jVtl09dd747dq8Dh/PfBJHjx6Ft7d3jY4pKyvT+ffKy8sTNVdXV/HvNWLEiBr/exEREenD4ExERHSTm0NZdHS0Tohu1aqVmMG8Uyh79NFHsX33PiyO2ng/2m60ystK8eRQH7zz9tuYO3fubferj19uEBER1VRtcijXNxERUZNnbm6O4OBgBAcHo6ysDJs2bRIhOj09HUuWLMGSJUvuuAz40uXLaN3ey0DPovEwM7eAi5sH0tLSqtXqezk9ERFRfWBwJiKiZsXc3ByBgYEIDAysduGpzMxMLFu2DMuWLbvlhacKCgpg39LV0E+hUbC0sRWhuKSkBGvXrr3lBdzc3d3FrcTq6gJuREREdY1LtYmIiHD9glTx8fF6b3W0LTERbXz64tn3Fhuw08bhzYdC0dreBi4uLvf9lmFEREQ1wc84ExER3YOKigokJCRAlmVERkYiJycHAGBsYoLRkx+4Y3DOy8nGqq8+wf7EeORmZ8PG3h6eXbph6vMvo0uf/rXqpeDaVXz56vM4f+IYCnKvwd7REQPGTMT0OW/AysYWAPDnN4vx13efVzvW3NISv+9Pve3YhXm5WP7B29gTvwEA0H/MBDz11vuwtrO/ZR9zJo3H1Ywr+HXXsVvuc7O5UgBOHz4gvm7btq2YWR44cCDDMhERGRw/40xERHQPTE1NMWHCBEyYMAFLlizBli1bIMsyfv31PzU6/tPZT6GyshLPL/oKrm08kZeThcM7tqMwL7fWvaiMjDBg7EQ8+MJc2LV0RPqFs/hx4TwUvpOLlz5bAgAIefJZTJj2qM5xC554AB179NY79pevzERO+hW89eNKAMCy+a/hq9dmYd6yX6vt+91bL8OzizeuZlypce/W1tZ49tlnIUkSBgwYAJVKVeNjiYiIGhIGZyIiIj1MTU0xfvx4jB8/Hvv3H7jj/kX5eTi2dxcW/hqO7gOHAABc3D3QqWefu3p8G3sH+D34mPjaxd0Dfg8+huifl4ptltbWsLS2Fl+fO56CS6dPYsaCj2877qXUU9ifmIBFf8aic6++AIBn3/sUb0wLxuUzp+Hu1VHsu27Vv1Gcnw9p5kvYvy2+Rn2bmJhAkiR8+umnNX6uREREDRWDMxERUU3VYMLUwsoaFlbW2LV5HTr37gtTM/Nq+7z/r+k4tjdZ7zgr952+5farGelI3rgW3QcMue2xm+Tf4dbOC936D7rtPicO7IGVrZ0IzQDQuXc/WNna4cT+PSI4Xzx9EvKSL/DRn7HIuHhBb883U6lUnGEmIqImg8GZiIioDhmbmOD5RV9i2fxXseGP/6B9tx7oPmAIhgWGol2XbgCAZ99fjPLS0lqN+/mcZ7E7fj3KS0vRf/R4PPv+rT9nXVFehsTYSEz+10y94+VmZcG+pVO17fYtnZCbnSXG+uLl5/Doq2/D2c2jVsGZiIioKWFwJiIiqmNDJgain+9YHNuTjBMH9uJAYgKili/Bs+8txpgpU+Ho2rrWYz7xxrt44Pk5SDubipVffIRfPnoXT7+zqNp+OzesQUlRIUaFSncc81YTwgoUMbP+22eL4NGhI0aFhNW6XyIioqaEwZmIiKgemJlboNewUeg1bBQemDkHS956GX9+ez04381S7RbOLmjh7AIPr06wdWiBt6ZPhvTsi2jhontf6c2aVejnOw4tnF30ju/g7IzcnOxq2/Ov5sDB0RkAcCR5Oy6cPA5pfZvrxf/eiOPxIT0QNmM2ps1+Ve9jEBERNRUMzkRERPeBR4fO2LVpHYC7W6p9sxs3kqwoL9fZnnHpAo4kJ+H1Jb/ccYwuvfujuCAfpw7tFxcuO3lwH4oL8sUts179+iedPk8fPoDv3pyD93+LRKu27e66fyIiosaGwZmIiKgOFVy7isUvzsCYsGnw7OINS2sbpB45iOjlSzBg7EQAqNVS7b1bNyMvOwsdfXrDwsoaF1NP4j+L30fXvgPg4tFGZ9/48D/QwtkVfUaOqTbOqUP78fXc2Vjwy19wdG0Njw6d0GfEaCx9+1U88+71q28vnf8a+vmOExcG+2c4/v/27jyuqjr/4/j7IrLIpuCCBIYbSq65o+aGey4oXLWcyqyZNLMazVansZpptRrTbLfl16JeFEXEHbc0NU3TzCwdTc0FFQUE2e/vj6bTMOIRDDkgr+fj4WO853vuOZ/LH0wvz7n3pp1LkSQFN2x8xe9xBgDgekI4AwBQijy8vNS45c1K+OhdnTz6s/LzchUQGKTe9tEaft/EEh/Pzd1Dqx2f6cMXpykvJ0cBgUHq2HeAhv/5gUL7FRQUaG3cPPUYNkJVqlS55DjZFy/q+KGDys/NM7Y99Moszfnn3/TsPbdJktr36qt7//bPEs8IAMD1zuZ0/nbDl3XS0tLk5+en1NRU+fr6Wj0OAABFat+hg6qHNtb454r+RGv8burtQ9WpVXPNmTPH6lEAAChSSTrUpYxmAgAAAACgQiKcAQAAAAAwQTgDAAAAAGCCcAYAAAAAwAThDAAAAACACcIZAIBS8vy4OzXt7hFFru3fuV3RTYP07727S3TMc8mn9Prk+zWxf1fFhN+gOc8/fck+q+Z/pqmjo3Rnh3Dd2SFc0+4eoZ927yz2OU78fEij2zTWHe2bFtq+ZWWinhk7UndHNNef2obpiZGDtXPjuhLNDwDA9YBwBgCglETG3KbvtmxS8i/HLllLWjhX9cObqUGzliU6Zm5Ojnz9AxQ97iGFNr2pyH32btusrrdG6ZmPHXp+brxq1b1Bz95zm86eOnHF4+fl5ur1yfcrvF3HS9a+375FrTp301PvfqqXFyxX846d9eL9d+nf3+8p0WsAAKCiI5wBACgl7Xr0kV9ATa2Lm1doe/bFTG1KjFev6NtKfMzawSG656nn1CPKrmreRX/H5MPT31T/28eofnhzBTdorHHPTZezoEB7vvryisf/YsZLuqFBI3XuP/iStbFPPquoeyeoUYvWCgptoNGTnlDgjfW1fe2qEr8OAAAqMlerBwAA4HpRxdVV3YfGaG3cfNknTJLNZpMkbV6eoLzcXHUbPFySNLpNI9PjhLftqKnvfXbVc+RcvKj8vDx5+1U33W/Pli+1eXmCXl20SltWJl7xuAUFBcrKuHDF4wIAcL0hnAEAKEW9okdp8Qdv6butm9WiUxdJUtKCuerYZ4ARnNPjzK/Yunl4/KEZPn3tn/KvE6iWnW+57D7p51I064mH9eDLs1TN26dYx43/8G1lZV5UlwFD/tB8AABUNIQzAAClKLhBYzW5uZ2SFs5Vi05ddPLIYe3bsVV/++ALY5+6N9a/Zudf9P6b+nLpYj3zSazc3C8f4G89PUVdBw1Ts/adinXcjQlxmj/rVT325ofyC6hZWuMCAFAhEM4AAJSyyJjb9P5zT+nPTz+vpIXzVCsoWC0jfr/6e61u1V78wVta8M5M/X3OPIU2KfqDxH6zZ8smfZ20UvFz3v51g9OpgoIC2ZuFaNyzLyvyv96PvSlxsWZPnaxH/vWuWnXuVuK5AACo6AhnAABKWef+QzTnn09rY0Kc1i2ar9720cb7naVrc6v2og9ma8FbM/S39z9Xoxatrrj/C3OXqCA/33i8LWmFFr33pp7/Il7+dQKN7RsT4jT7qcl6+NU31bZH7xLPBQDA9YBwBgCglHl6eanLwCH6/PUXlZmepp7DCn+3c0lv1T607ztJUlZmhtJSzurQvu/kWtVNIY3CJP16e/YXM17Rw9PfVK0bQnTudLIkyaOalzy9vCRJiZ/O0bbVyzXto/mSpOCGjQud48B338rm4qJ6Yb9/l/PGhDjNfPwhjX3yWYW1amsc183DQ14+RX/C928KCgqUmZlZotcJAEB5RTgDAHANREbfpjWxX6hVl+6qFRT8h471yLC+xt8P7t2tjQlxqhUUrLeTtkmSln/+sfJyczT9oT8Xet6ICZM0cuIjkn79MLCTRw6X6Lyr5n2q/Lw8vffsk3rv2SeN7T2iRmjii/8yfW5+fr7mzZunY8eOyW63Kzo6WsHBf+znAACAVWxOp9Np9RBpaWny8/NTamqqfH3N/wUbAACrtO/QQdVDG2v8c9OtHqXce3zErfpp985C2yIiImS32xUTE6OQkBCLJgMA4Fcl6VCXMpoJAABUIq6urho5cqRmzJihrl27ymaz6auvvtKkSZNUr149RURE6LXXXtPPP/9s9agAAFwR4QwAQDG52FwKfaAWLq8gP1/e3t568MEHtXHjRh07dkxvvPGGunXrJpvNpi1btmjy5MkKDQ1Vx44dNX36dB0+fNjqsQEAKBLhDABAMflV91NGerrVY1QIGem/3v72m6CgIE2cOFHr16/XL7/8olmzZql79+6y2Wzatm2bpkyZovr166t9+/Z6+eWXdejQIQunBwCgMMIZAIBiCmvcWIe/36Ny8PEg5Vr6+XM6ceSwGjZsWOR63bp1NWHCBK1bt07Hjx/X7Nmz1bNnT7m4uGj79u167LHH1KBBA7Vr104vvfSSDh48WMavAACAwghnAACKKTo6Wqd+OaoDe3ZZPUq5tm3NchXk52vYsGFX3DcwMFDjx49XUlKSjh8/rrfeekuRkZFycXHRjh079Pjjj6tRo0Zq06aNXnjhBR04cKAMXgEAAIXxqdoAABRTfn6+6gYFqUGrtpr8r3dVpUoVq0cqdy5euKC/3TFcwbX8tWH9+qs+zunTpxUXFyeHw6G1a9cq/7/eW96qVSvZ7XbZ7XaFhYWVxtgAgEqoJB1KOAMAUAIOh0O33Xabut4apfuefVnuHp5Wj1RupJ9L0YsT7tYvB/Zr9apV6tChQ6kc98yZM1q0aJEcDofWrFlTKKJbtmxpfMVV06ZNS+V8AIDKgXAGAOAamj9/vm6//Xa5eXioTffeat21h/z8A1TV3d3q0cqU0+lUTlaWziWf0va1K/Xt5g3y9PQs1Wj+X2fPntWiRYsUGxur1atXKy8vz1hr3ry5cSU6PDz8mpwfAHD9IJwBALjGfvrpJ82fP1/z5zu0e/e3Vo9jKZvNpi5dumrEiF+v/NatW7dMzpuSkqLFixfL4XBo9erVys3NNdZuuukmI6KbNWtWJvMAACoWwhkAgDKUmZmpc+fOKScnx+pRypyHh4f8/f3lbvHV9nPnzik+Pl4Oh0MrV64sFNHh4eHG7dzNmzeXzWazcFIAQHlBOAMAgErr/Pnzio+PV2xsrFasWFHoHzSaNGliXIlu0aIFEQ0AlRjhDAAAICk1NVVLliyRw+HQihUrlJ2dbayFhYUpJiZGdrtdrVq1IqIBoJIhnAEAAP5HWlqaEhIS5HA4tGzZskIR3ahRI+N27ptvvpmIBoBKgHAGAAAwkZ6eroSEBMXGxioxMVFZWVnGWsOGDY0r0W3atCGiAeA6RTgDAAAU04ULF7R06VI5HA4lJibq4sWLxlr9+vWNiG7Xrh0RDQDXEcIZAADgKmRkZCgxMVEOh0NLly5VZmamsRYaGqqYmBjFxMSoQ4cORDQAVHCEMwAAwB+UkZGhZcuWKTY2VgkJCcrIyDDW6tWrZ1yJ7tixIxENABUQ4QwAAFCKMjMztXz5cjkcDi1ZsqRQRIeEhCg6Olp2u12dOnWSi4uLhZMCAIqLcAYAALhGLl68qBUrVsjhcCg+Pl4XLlww1m644Qbjdu7OnTsT0QBQjhHOAAAAZSArK0srVqxQbGys4uPjlZaWZqwFBQUZV6K7dOlCRANAOUM4AwAAlLHs7GytXLlSDodDixcvLhTRdevW1fDhw2W329W1a1dVqVLFwkkBABLhDAAAYKns7GytXr1aDodDixYtUmpqqrEWGBhoRPQtt9xCRAOARQhnAACAciInJ6dQRJ8/f95Yq127thHR3bp1k6urq3WDAkAlQzgDAACUQzk5OUpKSjIiOiUlxVirVauWhg0bJrvdrh49ehDRAHCNEc4AAADlXG5urtauXSuHw6G4uDidPXvWWKtZs2ahiK5ataqFkwLA9YlwBgAAqEByc3O1bt06I6LPnDljrAUEBCgqKkp2u129evUiogGglBDOAAAAFVReXp7Wr18vh8OhhQsX6vTp08ZajRo1jIiOjIyUm5ubhZMCQMVGOAMAAFwH8vLytHHjRjkcDi1YsEDJycnGWvXq1Y2I7t27NxENACVEOAMAAFxn8vPzC0X0qVOnjDU/Pz8NHTpUdrtdffr0kbu7u4WTAkDFQDgDAABcx/Lz87Vp0yYjok+cOGGs+fr6asiQIbLb7erbt688PDwsnBQAyi/CGQAAoJIoKCjQ5s2b5XA4FBsbq+PHjxtrPj4+RkT369ePiAaA/0I4AwAAVEIFBQX66quvjIj+5ZdfjDVvb28NHjxYdrtd/fv3l6enp4WTAoD1CGcAAIBKrqCgQFu3bjUi+ujRo8aat7e3Bg0apJiYGA0YMEDVqlWzcFIAsAbhDAAAAENBQYG2bdum2NhYORwOHTlyxFjz8vLSrbfeKrvdrgEDBsjLy8vCSQGg7BDOAAAAKJLT6dTXX39tXIk+fPiwsVatWjUNHDhQdrtdt956KxEN4LpGOAMAAOCKnE6nduzYIYfDIYfDoUOHDhlrnp6eGjhwoGJiYjRo0CB5e3tbOCkAlD7CGQAAACXidDr1zTffGLdzHzx40Fjz8PDQgAEDZLfbNWjQIPn4+Fg4KQCUDsIZAAAAV83pdGrXrl3GlegDBw4Ya+7u7urfv7/sdrsGDx7Mf7sBqLAIZwAAAJQKp9Op3bt3GxH9448/Gmvu7u7q16+fYmJiNGTIEPn5+Vk4KQCUDOEMAACAUud0OrVnzx7jdu4ffvjBWHNzc1Pfvn1lt9s1ZMgQVa9e3bpBAaAYCGcAAABcU06nU3v37jWuRO/bt89Yq1q1qvr06SO73a6hQ4eqRo0aFk4KAEUjnAEAAFCmvv/+eyOi9+7da2yvWrWqevfurZiYGEVFRcnf39/CKQHgd4QzAAAALLNv3z7jdu49e/YY211dXRUZGSm73a6oqCgFBARYOCWAyo5wBgAAQLmwf/9+40r07t27je1VqlRRr169ZLfbNWzYMNWsWdPCKQFURoQzAAAAyp0ff/zRuBK9a9cuY3uVKlXUs2dPxcTEaPjw4apVq5Z1QwKoNAhnAAAAlGsHDhwwIvqbb74xtru4uKhHjx6y2+0aPny4ateubeGUAK5nhDMAAAAqjIMHDxoRvWPHDmO7i4uLunXrZkR0YGCghVMCuN4QzgAAAKiQDh06ZET0119/bWy32Wzq1q2bYmJiFB0drbp161o4JYDrAeEMAACACu/w4cNasGCBHA6Htm7damy32Wzq2rWr7Ha7oqOjFRQUZOGUACoqwhkAAADXlSNHjhhXords2WJst9ls6ty5sxHRwcHBFk4JoCIhnAEAAHDdOnr0qHElevPmzYXW/juiQ0JCLJoQQEVAOAMAAKBSOHbsmBYsWKDY2Fht2rRJ//2ftp06dZLdbldMTIzq1atn4ZQAyiPCGQAAAJXO8ePHjSvRX375ZaGI7tChgxHRoaGh1g0JoNwgnAEAAFCpnThxQgsXLpTD4dCGDRsKRXT79u2NiK5fv76FUwKwEuEMAAAA/MfJkye1cOFCxcbGav369SooKDDW2rZtK7vdLrvdrgYNGlg4JYCyRjgDAAAARTh16pTi4uLkcDi0bt26QhF98803GxHdqFEjC6cEUBYIZwAAAOAKTp8+bUT02rVrlZ+fb6y1bt3auJ07LCzMwikBXCuEMwAAAFACZ86cUVxcnGJjY7VmzZpCEd2yZUvjSnSTJk0snBJAaSKcAQAAgKt09uxZLVq0SA6HQ2vWrFFeXp6x1rx5cyOiw8PDLZwSwB9FOAMAAAClICUlRYsXL5bD4dCqVasKRXSzZs2M27mbNWtm4ZQArgbhDAAAAJSyc+fOafHixYqNjdXKlSuVm5trrIWHhxtXops1ayabzWbhpACKg3AGAAAArqHz588rPj5eDodDK1euVE5OjrHWtGlTxcTEyG63q0WLFkQ0UE4RzgAAAEAZSU1N1ZIlS+RwOLR8+fJCER0WFmbczt2qVSsiGihHCGcAAADAAmlpaVqyZIliY2O1bNkyZWdnG2uNGjUybudu3bo1EQ1YjHAGAAAALJaenq6EhAQ5HA4tW7ZMWVlZxlrDhg2N27nbtGlDRAMWIJwBAACAcuTChQtaunSpHA6HEhMTdfHiRWOtQYMGiomJUUxMjNq1a0dEA2WEcAYAAADKqQsXLigxMVGxsbFaunSpMjMzjbXQ0FDjSnT79u3LPKJ/++TwLVu2KCUlpdAnh1cWHh4eCggIUGRkpPr37y9PT0+rR8I1QjgDAAAAFUBGRoaWLVsmh8OhhISEQhFdr149I6I7dux4TSM6JSVFd989VsuWJSovL0+hTcLlU8Nfrm7u1+yc5VVuVpbOnT6lY/8+IC9vb42+/XbNnDlTbm5uVo+GUkY4AwAAABVMZmamli9fLofDoSVLligjI8NYCwkJMW7n7tSpk1xcXErtvCkpKYrs3VuHfj6imPEPq1PfW+VfJ7DUjl9RHT90UF8mLtbCd97QgAED5Jg/n3i+zhDOAAAAQAV28eJFLV++XLGxsYqPj9eFCxeMteDgYEVHR8tutysiIuIPR3Tv3r21fecu/f3D+bqxSfgfHf26s2P9Gr0y8R6NHzdOM2bMsHoclCLCGQAAALhOZGVlacWKFXI4HIqPj1d6erqxFhQUZER0ly5dShzRR48eVb169TTxpTfUY2hMaY9+3fi/V/+pDQvn6uSJE6patarV46CUlKRDS+8eDwAAAAClzsPDQ0OHDtWnn36q5ORkxcfH64477pCvr6+OHz+umTNnqlu3bgoODtbEiRO1YcMG5efnF+vYsbGxqurmpva9+l7jV1Gxdek/WClnz2rt2rVWjwKLEM4AAABABeHh4aHBgwfrk08+UXJyspYsWaI777xTfn5+OnHihGbNmqXu3bsrODhYEyZM0Lp160wjev369Qpv20FePtz1aab+TS0UULuO1q9fb/UosAjhDAAAAFRA7u7uGjRokD7++GMlJydr6dKlGjNmjKpXr66TJ09q9uzZ6tmzp4KCgjR+/HglJSUpLy+v0DHOnk1R9Vp1LHoFFYfNZlP1mrWVkpJi9SiwCOEMAAAAVHBubm4aOHCgPvzwQ506dUrLli3T2LFjVaNGDSUnJ+vtt99WZGSkgoKCNG7cOK1Zs0Z5eXnKys6Sm3vl+8qpq+Hm4aHs7Gyrx4BFCGcAAADgOuLm5qb+/fvrgw8+0KlTp7R8+XLdc8898vf31+nTp/XOO++od+/eqlu3ro4cOWL1uECF4Gr1AAAAAACujapVq6pfv37q16+f3nrrLa1bt04Oh0NxcXE6c+aMqrgWLwdSz57RFzNe1s6NSTp/5oy8/fx0Y5ObNPKByWpyc7sSzXT4h71a+O4s/fDNNqWfO6daNwSr76g7NejOe4195s2crvlvvnbJc909PfX5zoNXPEduTrYeH3GrDv/wvabHrVT98OaX7JN+LkWTovoo5dQJfbJtn7x8/Ur0OlC5EM4AAABAJVC1alX16dNHffr00ezZs7V+/XqN/tOfivXcVx68V3l5eXrghRmqE3KjUs+e1p6vvtSF1PMlnuPg3t3y8w/QQy/PUkDdIO3fuV1vPz1FLi4uGvinsZKkIWPHq++oOws9b9rdI9SoeetineOTV/6hGrUDdfiH7y+7z5tTJ+vGJuFKOXWixK8BlQ/hDAAAAFQyrq6uioyMVEhIyBX3zUhL1b4d2/TsJwvUrEOEJKn2DcFq3PLmqzp3ZPRthR4HhtyoH3dt19ZVy4xw9vTykqeXl7HP4R/26tiBH3XftJeuePxvNiTp203rNeWN97VzQ1KR+yz/4mNlpqXJPuGvl90H+G+EMwAAAIDL8qjmJY9qXtq2ZrnCWrdRVbdLP0zsH38erX07tpoe57NvDlx2LTM9Xd5+1S+7vtrxuYJCG+imdh1Nz3H+zGm99bcpemzWHLl7eBa5z9EDP8ox+3W9OC9Bp47yHm8UD+EMAAAA4LKquLrqgRf+pbefnqKVc/9P9W9qrmbtI9Tl1qEKbXKTJGn8P6YrJyvrqo6/f+d2bV6+RE++/UmR67k52dqYEKdhf55gehyn06lZTzysfqPuUKMWrZR87GiRx3p98v26c8rfVCsomHBGsRHOAAAAAExF9LtVbXtEat/2rdq/a4d2bVyrRR/M1vjnpqvX8JEKqFP3qo575Kf9enHC3bLf/1e16tK9yH22rEzUxYwL6j7UbnqsxP/7QJkX0jXsLxMvu8+nr76g4IaN1H1I9FXNi8qLcAYAAABwRW7uHmrVpbtademuERMmafbUyZo369dwvppbtY8e+FHTxtjV2z5aMeMfvuzz1sR+obY9eqtGrdqmx9+zdZN++vYbjWoZWmj7ozED1G3QcE18aYa+2/qljvz4g+wr/vPebqdTkjQmormi73tQox6cYnoOVF6EMwAAAIASC24Ypm2rl0sq+a3aR37ar2lj7OoRZdfovz5+2f1OHTui77Zu0uOzP7riMe956jnd/tBjxuOU5JN67t7bNem1txXW6tcPMpvyxvuF5jywZ5fefGqS/vFpnALrhRZ7flQ+hDMAAACAy0o/l6LpD9+nXtGjdGOTcHl6eevgd99q8Qez1T6ynySV6FbtIz/t19/vilHrLt01eMx9Onc6WZLkUqWK/PwDCu2btGCuatSqo5u79brkOD/t3qk3HntQ0z6ar4A6dVUrKLjQuke1Xz+VO7DejQoIDPrP30ML7ZN2LkWSFNywMd/jDFOEMwAAAIDL8vDyUuOWNyvho3d18ujPys/LVUBgkHrbR2v4fZd/P/HlfLV8idJSzmrDkoXasGShsb1WULDeTtpmPC4oKNDauHnqMWyEqlSpcslxsi9e1PFDB5Wfm3d1LwwoAZvT+Z8b+y2UlpYmPz8/paamytfX1+pxAAAAgEqhfYcOqh7aWOOfm271KOXe1NuHqlOr5pozZ47Vo6CUlKRDXcpoJgAAAAAAKiTCGQAAAAAAE4QzAAAAAAAmCGcAAAAAAEwQzgAAAAAAmCCcAQAAABTp+XF3atrdI4pc279zu6KbBunfe3eX6JhbVibqmbEjdXdEc/2pbZieGDlYOzeuu+z+Xy5dpOimQXpxwt2mx00+dlTRTYMu+bNz49pC++XmZOuz11/Ufb3aa2SLUN3fJ0JrFnxRoteAyofvcQYAAABQpMiY2/TKxHuV/Msx1b4huNBa0sK5qh/eTA2atSzRMb/fvkWtOnfT6L8+oWo+vlq7cJ5evP8uvTAvQQ1ualFo3+Rfjunjl59TeLuOxT7+3z+cp5BGTYzH3n7VC62/+vB9On/2jO7/x6uqW6++UlPOKD+P74KGOcIZAAAAQJHa9egjv4CaWhc3TyMemGxsz76YqU2J8br9r4+X+Jhjn3y20OPRk57QtqQV2r52VaFwzs/P14wpEzRy4mTt275NGempxTq+T/UaqlGrdpFrOzeu1d6vt2j2qq/kU72GJKl2cEiJXwMqH8IZAAAAQJGquLqq+9AYrY2bL/uESbLZbJKkzcsTlJebq26Dh0uSRrdpZHqc8LYdNfW9z4pcKygoUFbGhUuuDDvefE2+/gHqHXO79m3fVuyZX7x/jHKys1X3xvoafNdfFNF/kLH2ddJKNWzeUos+mK0NixfI3bOa2vfqo1EPPSp3D89inwOVD+EMAAAA4LJ6RY/S4g/e0ndbN6tFpy6SpKQFc9WxzwAjdqfHrTI9hpuHx2XX4j98W1mZF9VlwBBj2w/fbNOaBXP16qKVxZ7Tw6uaxjw+TU3btJfN5qKv167Qa5PG6YGcGeo+JFqSdOroz/phx9dyc/PQo7M+UNq5FL33zBO6kHpeE55/vdjnQuVDOAMAAAC4rOAGjdXk5nZKWjhXLTp10ckjh7Vvx1b97YPfP1Cr7o31r+rYGxPiNH/Wq3rszQ/lF1BTknTxwgXNmDJR4597Rb41Aop9LN8aARo85i/G40YtWikjNVWL3p9thLOzoEA2m00PTZ8lLx9fSVLu49M0/aE/696nn+eqMy6LcAYAAABgKjLmNr3/3FP689PPK2nhPNUKClbLiFuM9au5VXtT4mLNnjpZj/zrXbXq3M3YfvLoYSX/clQvjL/L2OYsKJAk2ZuFaOayjQqsF1qsucNat9Wa2N8Dv0atOvKvE2hEsyQFN2wsp9OpsydPKCi0QbGOi8qHcAYAAABgqnP/IZrzz6e1MSFO6xbNV2/7aOP9zlLJb9XemBCn2U9N1sOvvqm2PXoXWruhQSO9Hp9UaNvnM15SVkaGxj75rAICg4o996Hv96j6f31QWJM27bV5xRJdzMiQp5eXJOn44YNycXFRQGDdYh8XlQ/hDAAAAMCUp5eXugwcos9ff1GZ6WnqOazwdzuX5FbtjQlxmvn4Qxr75LMKa9VW504nS/o1rr18fOXm7qF6YU0LPcfLx0+SCm1P/HSOtq1ermkfzZckrY2bL1dXV9W/qYVsNpu2r12lxE/n6E+TnzKec8ugYYp963W9+eRfNXLiI0o7l6JPXv6HekWP4jZtmCKcAQAAAFxRZPRtWhP7hVp16a5aQcFXfsJlrJr3qfLz8vTes0/qvWefNLb3iBqhiS/+q9jHST+XopNHDhfaFvv2DJ0+fkwuLlUUFNpA9//zNeP9zdKv/wDw9Jy5+uAfU/VoTH/5VK+hzv2H6LaHH73q14PKweZ0Op1WD5GWliY/Pz+lpqbK19f3yk8AAAAA8Ie179BB1UMba/xz060epdybevtQdWrVXHPmzLF6FJSSknSoSxnNBAAAAABAhUQ4AwAAAJWUW1U35ebkWD1GhZCbk62qVataPQYsQjgDAAAAlZS/fw2lpZy1eowKIS0lRTVq1LB6DFiEcAYAAAAqqYiICP2wY5uysy5aPUq5duzgT0o+fkwRERFWjwKLEM4AAABAJWW323UxM0M7N6y1epRybfPyJfL28VG/fv2sHgUWIZwBAACASqpx48Zq1669/u+VZ3X6+DGrxymXftq9UwkfvaPo4cPl4eFh9TiwCOEMAAAAVGKxsQ55uFbRtLtitGVlIrdt/8eF1PNas+ALPXfPKLVs3kIzZ860eiRYiO9xBgAAACq5n3/+WcOHR+ubb3bIs5qXwtt3km+NALm5u1s9WplyOp3Kyc5SyqmT2rdjq/Lz8jRgwEDNnfuFfHx8rB4PpawkHUo4AwAAAJAk7d+/Xw6HQ1999ZVSUs4pJzfX6pHKnKeHh2rWDFBkZKSio6MVFBRk9Ui4RghnAAAAAABMlKRDeY8zAAAAAAAmCGcAAAAAAEwQzgAAAAAAmCCcAQAAAAAwQTgDAAAAAGCCcAYAAAAAwAThDAAAAACACcIZAAAAAAAThDMAAAAAACYIZwAAAAAATBDOAAAAAACYIJwBAAAAADBBOAMAAAAAYIJwBgAAAADABOEMAAAAAIAJwhkAAAAAABOEMwAAAAAAJghnAAAAAABMEM4AAAAAAJggnAEAAAAAMEE4AwAAAABggnAGAAAAAMAE4QwAAAAAgAnCGQAAAAAAE4QzAAAAAAAmCGcAAAAAAEwQzgAAAAAAmCCcAQAAAAAwQTgDAAAAAGCCcAYAAAAAwAThDAAAAACACcIZAAAAAAAThDMAAAAAACYIZwAAAAAATBDOAAAAAACYIJwBAAAAADBBOAMAAAAAYIJwBgAAAADABOEMAAAAAIAJwhkAAAAAABOEMwAAAAAAJghnAAAAAABMEM4AAAAAAJggnAEAAAAAMEE4AwAAAABggnAGAAAAAMAE4QwAAAAAgAnCGQAAAAAAE4QzAAAAAAAmCGcAAAAAAEwQzgAAAAAAmCCcAQAAAAAwQTgDAAAAAGCCcAYAAAAAwAThDAAAAACACcIZAAAAAAAThDMAAAAAACYIZwAAAAAATBDOAAAAAACYIJwBAAAAADBBOAMAAAAAYIJwBgAAAADABOEMAAAAAIAJwhkAAAAAABOEMwAAAAAAJghnAAAAAABMEM4AAAAAAJggnAEAAAAAMEE4AwAAAABggnAGAAAAAMAE4QwAAAAAgAnCGQAAAAAAE4QzAAAAAAAmCGcAAAAAAEwQzgAAAAAAmCCcAQAAAAAwQTgDAAAAAGCCcAYAAAAAwISr1QNIktPplCSlpaVZPAkAAAAAoDL4rT9/61Ez5SKc09PTJUkhISEWTwIAAAAAqEzS09Pl5+dnuo/NWZy8vsYKCgp0/Phx+fj4yGazWT0OrmNpaWkKCQnR0aNH5evra/U4APCH8XsNwPWG32soK06nU+np6QoKCpKLi/m7mMvFFWcXFxcFBwdbPQYqEV9fX34RA7iu8HsNwPWG32soC1e60vwbPhwMAAAAAAAThDMAAAAAACYIZ1Qq7u7u+vvf/y53d3erRwGAUsHvNQDXG36voTwqFx8OBgAAAABAecUVZwAAAAAATBDOAAAAAACYIJwBAAAAADBBOAMAAAAAYIJwRqUye/Zs1a9fXx4eHmrbtq02btxo9UgAcNU2bNigwYMHKygoSDabTYsWLbJ6JAC4ai+88ILat28vHx8f1a5dW1FRUdq/f7/VYwGSCGdUIvPmzdPDDz+sp556Sjt37tQtt9yiAQMG6MiRI1aPBgBXJSMjQ61atdKsWbOsHgUA/rD169drwoQJ2rJli1atWqW8vDz17dtXGRkZVo8G8HVUqDw6duyoNm3a6K233jK2hYeHKyoqSi+88IKFkwHAH2ez2RQXF6eoqCirRwGAUnH69GnVrl1b69evV7du3aweB5UcV5xRKeTk5GjHjh3q27dvoe19+/bV5s2bLZoKAAAAl5OamipJ8vf3t3gSgHBGJXHmzBnl5+erTp06hbbXqVNHJ0+etGgqAAAAFMXpdGrSpEnq2rWrmjdvbvU4gFytHgAoSzabrdBjp9N5yTYAAABY64EHHtDu3bv15ZdfWj0KIIlwRiVRs2ZNValS5ZKry8nJyZdchQYAAIB1Jk6cqPj4eG3YsEHBwcFWjwNI4lZtVBJubm5q27atVq1aVWj7qlWr1LlzZ4umAgAAwG+cTqceeOABLVy4UElJSapfv77VIwEGrjij0pg0aZLuuOMOtWvXThEREXr33Xd15MgRjRs3zurRAOCqXLhwQQcOHDAeHzp0SLt27ZK/v7/q1atn4WQAUHITJkzQ559/rsWLF8vHx8e4U9DPz0+enp4WT4fKjq+jQqUye/Zsvfzyyzpx4oSaN2+u119/na83AFBhrVu3Tj179rxk+1133aWPPvqo7AcCgD/gcp878+GHH2rMmDFlOwzwPwhnAAAAAABM8B5nAAAAAABMEM4AAAAAAJggnAEAAAAAMEE4AwAAAABggnAGAAAAAMAE4QwAAAAAgAnCGQAAAAAAE4QzAAAAAAAmCGcAAK6RadOmqXXr1laPAQAA/iDCGQCAq2Cz2Uz/jBkzRo888ojWrFljyXwLFixQx44d5efnJx8fHzVr1kyTJ0821ol6AACKz9XqAQAAqIhOnDhh/H3evHl6+umntX//fmObp6envL295e3tXeazrV69WqNGjdLzzz+vIUOGyGaz6fvvv7cs4gEAqOi44gwAwFUIDAw0/vj5+clms12y7X+v6o4ZM0ZRUVF6/vnnVadOHVWvXl3PPPOM8vLyNGXKFPn7+ys4OFhz5swpdK5ffvlFI0eOVI0aNRQQEKChQ4fq8OHDl50tISFBXbt21ZQpU9SkSROFhYUpKipKM2fOlCR99NFHeuaZZ/Ttt98aV8g/+ugjSVJqaqr+8pe/qHbt2vL19VWvXr307bffGsf+7TW98847CgkJUbVq1WS323X+/PnS+tECAFDuEM4AAJShpKQkHT9+XBs2bNBrr72madOmadCgQapRo4a2bt2qcePGady4cTp69KgkKTMzUz179pS3t7c2bNigL7/8Ut7e3urfv79ycnKKPEdgYKD27t2r7777rsj1kSNHavLkyWrWrJlOnDihEydOaOTIkXI6nbr11lt18uRJJSYmaseOHWrTpo0iIyOVkpJiPP/AgQOaP3++lixZouXLl2vXrl2aMGFC6f+wAAAoJwhnAADKkL+/v9544w01adJEY8eOVZMmTZSZmaknn3xSjRs31hNPPCE3Nzdt2rRJkjR37ly5uLjo/fffV4sWLRQeHq4PP/xQR44c0bp164o8x8SJE9W+fXu1aNFCoaGhGjVqlObMmaPs7GxJv99G7urqalwh9/T01Nq1a7Vnzx45HA61a9dOjRs31vTp01W9enXFxsYax8/KytLHH3+s1q1bq1u3bpo5c6bmzp2rkydPXvOfHwAAViCcAQAoQ82aNZOLy+//91unTh21aNHCeFylShUFBAQoOTlZkrRjxw4dOHBAPj4+xnum/f39lZWVpYMHDxZ5Di8vLy1dulQHDhzQ1KlT5e3trcmTJ6tDhw7KzMy87Gw7duzQhQsXFBAQYJzL29tbhw4dKnSuevXqKTg42HgcERGhgoKCQu/xBgDgesKHgwEAUIaqVq1a6LHNZityW0FBgSSpoKBAbdu21WeffXbJsWrVqmV6roYNG6phw4a699579dRTTyksLEzz5s3T3XffXeT+BQUFqlu3bpFXsqtXr37Z89hstkL/CwDA9YZwBgCgHGvTpo3mzZtnfFjX1QoNDVW1atWUkZEhSXJzc1N+fv4l5zp58qRcXV0VGhp62WMdOXJEx48fV1BQkCTpq6++kouLi8LCwq56PgAAyjNu1QYAoBwbPXq0atasqaFDh2rjxo06dOiQ1q9fr4ceekjHjh0r8jnTpk3To48+qnXr1unQoUPauXOnxo4dq9zcXPXp00fSryF96NAh7dq1S2fOnFF2drZ69+6tiIgIRUVFacWKFTp8+LA2b96sqVOnavv27cbxPTw8dNddd+nbb7/Vxo0b9eCDD2rEiBEKDAwsk58JAABljXAGAKAcq1atmjZs2KB69epp+PDhCg8P19ixY3Xx4sXLXoHu3r27/v3vf+vOO+9U06ZNNWDAAJ08eVIrV65UkyZNJEnR0dHq37+/evbsqVq1aumLL76QzWZTYmKiunXrprFjxyosLEyjRo3S4cOHVadOHeP4jRo10vDhwzVw4ED17dtXzZs31+zZs8vk5wEAgBVsTqfTafUQAACgYpg2bZoWLVqkXbt2WT0KAABlhivOAAAAAACYIJwBAAAAADDBrdoAAAAAAJjgijMAAAAAACYIZwAAAAAATBDOAAAAAACYIJwBAAAAADBBOAMAAAAAYIJwBgAAAADABOEMAAAAAIAJwhkAAAAAABP/D1fTd8perkTeAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "期权价格: 6.245708445206439\n"
     ]
    }
   ],
   "source": [
    "# 测试\n",
    "S = 50\n",
    "K = 52\n",
    "r = 0.05\n",
    "T = 2.0\n",
    "sigma = 0.3\n",
    "n = 2\n",
    "\n",
    "price = binomial_tree_price(S, K, r, T, sigma, n, option=\"put\", option_type=\"european\")\n",
    "print(\"期权价格:\", price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
